Неопределенный интеграл

2005

Неопределенный интеграл. Задания и ответы Сирота Ю.Н.

Сирота Ю.Н. СПбГУАП 01.01.2005

2005

Indefinite Integral. Cases and answers Yury Sirota

Yury Sirota Saint Petersburg State University of Aerospace Instrumentation 01.01.2005

Вариант 1

Вариант 3


1 1 1) −15 sin(3x) − 5 √ + 35 √ dx, x 16 −
49x2
1 2) (−50 + 38x + 42x2 )e6x dx, 3) −24  dx, arcctg x(6x)(1 + 36x2 )

x2 + 44x − 44 6x2 + 40x + 43 dx, 5) − dx, 4) 2 2
(x − 2)(x + 5)
(1 + x)(x − 8x + 20) √ −9x + 3x3 + 4x2 − 4 √ dx, 6) 2 21 − x2 − 4xdx, 7) −3 − x2 − 4x
5 cos x + 4 sin x + 7 dx, 8) − 2 (5 cos x + 3)(sin x + 1 + cos x)
2 sin x + 1 + cos x dx, 9) 8
16 cos2 x + 13 sin x cos x + 32 cos x + 11 sin x + 16 2 cos x + 6 sin x − 9 dx −5 cos x + 4 sin x cos x − 5 + 5 sin x 10)


1 1 1) 8 √ + 5 − 16e−4x dx, x 1 − 4x2

2) (1 − 4x − 9x2 ) ln(8x)dx, 3) −28 cos(7x)esin(7x) dx,

x2 + 17x + 72 25x2 − 26x + 11 4) 2 dx, 5) 1/3 dx, (x − 1)(x + 5)2 (x − 1)(x2 + 4x + 5)
√
258x + 15x3 + 131x2 + 76 √ 6) 2 −x2 − 2xdx, 7) dx, −21 − x2 − 10x
20 cos x + 7 sin x + 19 8) dx,
(5 cos x + 4)(sin x + 1 + cos x) 3 cos x + 7 sin x − 5 dx, 9)
cos2 x + 3 sin x cos x + 3 cos x + 2 + 2 sin x 15 cos x − 16 sin x − 7 dx 7 cos2 x + 11 sin x cos x + 20 cos x + 13 + 13 sin x

Вариант 4

10)

Вариант 2


1 1 1) 3 √ + 4 − 8 sin(4x)dx, x x

earcctg x(8x) dx, 2) (4 − 5x − 5x2 ) ln(6x)dx, 3) 48 1 + 64x2

x − 21 3x2 + 13x + 9 4) 2 dx, 5) 2 dx, 2 (x − 5)(−9 + x2 )
√
(1 + 2x)(x 2 + 4x +3 5) −63x − 67x − 15x + 41 √ 6) 2 x2 + 10x + 16dx, 7) dx, 10 + 6x + x2
7 cos x + 6 sin x + 8 8) − dx, 3 cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3
sin x + 7 + 7 cos x dx, 9)
cos2 x + 2 sin x cos x + 2 cos x + sin x + 1 −6 cos x + 7 + 2 sin x dx 4 cos2 x + 8 sin x cos x + 13 cos x + 9 sin x + 9 10)

2


1 1 1) 4 − 3 sin x − 8 √ dx, 1 − 4x2

x 1 dx, 2) (3 + x) arcctg x(3x)dx, 3) −18  √ arcsin(6x) 1 − 36x2

5x2 + 6x − 35 3x2 + 4x − 15 dx, 5) − dx, 4) 2 2
(x − 3)(x − 1)
(−1 + 2x)(x − 6x + 13) √ −12x3 + 58x2 − 54x − 9 √ 6) 2 x2 + 4x + 40dx, 7) dx, x2 − 6x + 8
6 cos x − 3 sin x + 5 8) dx,
3 cos2 x + 6 cos x − 4 sin x cos x − 3 sin x + 3 5 cos x + 11 sin x + 7 dx, 9) 2
(5 cos x + 3)(sin x + 2 + 2 cos x) 9 cos x + 5 sin x + 10 dx 4 cos2 x + 5 cos x − sin x + 1 10)

1

Вариант 5

Вариант 7


1 1 1) 4(1 + 4x2 )−1 + 4 + 3 √ dx, x x

1 2) (5 + 7x − 2x2 ) ln(9x)dx, 3) 16 √ dx, 1 − 4x2 arcsin(2x)

x2 − x − 38 5x2 + 48x + 54 4) dx, 5) dx, 2 2
(x − 2)(x + 4)
(3 + x)(x − 6x + 18) √ −9x3 + 43x2 + 14x − 13 √ 6) 2 −x2 + 4xdx, 7) dx, −x2 + 6x
7 cos x + 2 sin x + 2 8) − dx,
(5 cos x + 4) cos x −13 cos x + 3 sin x − 10 dx, 9) − 2
19 cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 −17 cos x + 21 sin x − 7 dx 40 cos2 x + 5 sin x cos x + 72 cos x + 32 + 7 sin x

−

Вариант 6

10)

10)

Вариант 8

10) 2


1) 8e−2x − 3 sin(3x) − 6 cos(3x)dx,

1 2) (−2 + 2x) arcsin xdx, 3) −16  dx, √ arccos(4x) 1 − 16x2

11x2 − 56x + 59 x2 + 16x + 33 dx, 5) 4) − dx, 2 2
√(x − 1)(x + 4)
(x − 3)(x − 34x + 13) −165x + 15x − 17x2 − 62 √ dx, 6) 2 −x2 + 10xdx, 7) 15 − x2 + 2x
cos x + 17 sin x + 5 dx, 8) − 1/2 4 cos2 x + 3 sin x cos x + 6 cos x + 2 + 2 sin x
−2 cos x + 13 sin x − 10 dx, 9) −
cos2 x + 4 sin x cos x − 4 cos x − 5 + 5 sin x 24 cos x + 19 sin x + 1 dx −10 cos2 x + 10 sin x cos x − 26 cos x + 11 sin x − 16


1 1) 2 − 12 sin(3x) − 4e−4x dx,
x
1 2) −(3 + x) arctg(5x)dx, 3) −9  dx, arctg(9x)(1 + 81x2 )

9x2 − 2x + 9 3x2 − 4x − 5 dx, 5) − dx, 4) 2 (x + 2)(x − 1)(x − 3) (1 + x)(x2 − 6x + 13)
√
10 + 20x + 21x2 + 9x3 √ 6) 2 −40 + 6x + x2 dx, 7) dx, 2 + 2x + x2
−14 cos x + 5 sin x − 7 8) − dx,
(5 cos x + 4)(sin x + 1 + cos x) −3 cos x + 3 sin x − 7 dx, 9) −
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 −3 cos x + 3 sin x + 2 dx −8 cos2 x + 4 sin x cos x − 15 cos x + 3 sin x − 7

−


1 1) 4 √ − 4e−2x + 2 cos(2x)dx, x

earcsin(6x) 2) (−17 − 24x − 14x2 )e−7x dx, 3) −48 √ dx, 1 − 36x2

61 − 74x + 33x2 3x2 − 7x + 42 dx, 5) dx, 4) 2
(−3 +2 2x)(13 + 6x + x 3)
(3√+ x)(x − 2)(x − 6) −26x + 18x + 33 + 6x √ 6) 2 x2 + 8x − 20dx, 7) dx, x2 − 6x + 10
3 cos x + 2 8) − 6 dx, (5 cos x + 4)(sin x + 1 + cos x)
7 cos x + 6 sin x + 3 dx, 9) cos
2 x + 2 sin x cos x + 2 cos x + sin x + 1 cos x + 5 sin x − 10 dx 8 cos2 x + 4 sin x cos x + 15 cos x + 7 + 3 sin x

4

10)

3

Вариант 9

Вариант 11


1) −3e−x + 20(1 + 16x2 )−1 − 8 cos(2x)dx,

cos(2x) dx, 2) −(1 + 2x) sin(3x)dx, 3) 4  sin(2x)

4x2 − 4x − 73 45x2 + 10x − 47 dx, 4) dx, 5) 2 2
(x − 3)(x + 4)
(1 + 3x)(x − 6x + 13) √ 58x − 9x3 + 34x2 − 21 √ 6) 2 7 − x2 + 6xdx, 7) dx, 12 − x2 + 4x
−7 sin x + 9 + 9 cos x 8) dx,
3 cos2 x + 6 cos x − 4 sin x cos x − 3 sin x + 3 13 cos x − 5 sin x + 1 dx, 9) −
cos2 x + 2 sin x cos x + 2 cos x + sin x + 1 4 cos x − 6 sin x − 3 dx 2 cos2 x + 6 sin x cos x + 10 cos x + 8 + 7 sin x −

Вариант 12

10)


1 1) −6 sin(3x) + 4 √ − 16 cos(4x)dx, 9 − 16x2

earcctg x(2x) 2) e−9x (69 + 23x + 18x2 )dx, 3) 12 dx, 1 + 4x2

2x2 − 7x − 70 7x2 − 36x + 34 4) − dx, 5) 1/3 dx, 2 2 (x − 1)(x − 6x + 10)
(x − 1)(x + 4)
√ −74x + 27x2 + 15x3 − 1 √ 6) 2 −16 − x2 − 10xdx, 7) dx, 8 − 2x − x2
sin x + 4 dx, 8) − (5 cos x + 3)(sin x + 1 + cos x)
21 cos x − 20 sin x + 29 dx, 9)
cos2 x + 4 sin x cos x − 4 cos x − 5 + 5 sin x 7 cos x + 44 sin x − 23 dx 18 cos2 x + 32 cos x + sin x cos x − sin x + 14

Вариант 10

10)


1 1 + 4 √ dx, 1) 40(16 + 25x2 )−1 + 2 √ x 1 −
4x2
2) (4 + 9x − 2x2 )e−x dx, 3) 32 cos(4x)esin(4x) dx,

x2 − 13x + 6 11x + 15 4) dx, 5) 2 dx, 2 2
(x − 4)(x − 1)
(x − 2)(x + 8x + 17) √ 9x + 16x2 + 12x3 − 10 √ 6) 2 x2 + 8xdx, 7) dx, 2 + 2x + x2
13 sin x − 21 − 21 cos x 8) − 1/2 dx, −3 cos2 x − 6 cos x + 4 sin x cos x + 3 sin x − 3
cos x + sin x + 7 dx, 9) −
cos2 x + 2 sin x cos x + 2 cos x + sin x + 1 −5 cos x + 6 sin x − 8 dx −2 cos2 x + 6 sin x cos x − 10 cos x + 7 sin x − 8 10)

6


1) −20(16 + 25x2 )−1 − 10 cos(2x) + 5 sin(5x)dx,

1 2) (−1 − 3x + 9x2 ) ln(5x)dx, 3) −32 √ dx, 1 − 64x2 arcsin(8x)

19x2 + 4x − 2 3x2 − 12x + 5 dx, 5) −2 dx, 4) (−2 + 3x)(x2 − 2x + 10)

(1 + x)(x − 4)(x − 3) √ −15x3 − 56x2 − 64x − 5 √ 6) 2 x2 + 8x + 15dx, 7) dx, x2 + 4x + 5
3 cos x − 4 sin x + 2 8) dx,
3 cos2 x + 6 cos x − 4 sin x cos x − 3 sin x + 3 3 cos x + 1 9) − dx,
cos2 x + 2 sin x cos x − 2 cos x + 3 sin x − 3 9 cos x + 4 sin x + 19 dx 24 cos2 x − 3 sin x cos x + 40 cos x + 16 − sin x 10) 2

5

Вариант 13

−


1 1) 8e4x + 12 √ + 16 sin(4x)dx, 9 − 16x2

cos(6x) dx, 2) −4(1 + x + x2 ) ln(7x)dx, 3) 36 sin(6x)

2x2 − x − 24 −43 − 18x + 13x2 4) 2 dx, dx, 5) − (x − 2)(x + 4)2 + 2x)(13 + 6x + x2 )
(1
√ 3 2 3x + 18x + 28x + 5 √ 6) 2 16 − 6x − x2 dx, 7) dx, −x2 − 4x
11 cos x + 4 sin x + 4 8) dx, (5
cos x + 4)(sin x − 1 − cos x) −25 cos x + 3 sin x − 15 dx, 9) − 2
16 cos2 x + 13 sin x cos x + 32 cos x + 11 sin x + 16 24 cos x + 28 sin x − 1 dx −20 cos2 x − 39 cos x + sin x − 19 10)

Вариант 14


1 1 1) −8(1 + 4x2 )−1 + 3 √ + 2 dx, x 1 − x2

1 2) (−1 + 3x) cos(2x)dx, 3) 10 dx, (1 + 25x2 ) arcctg x(5x)

2x2 − 21x + 24 14 + 8x + 3x2 4) dx, 5) 3 dx, 2
(3 + x)(x − 2)(x − 4)
(x + 2)(10 + 2x + x ) √ −3x3 − 16x2 − 21x + 1 √ 6) 2 −24 + 2x + x2 dx, 7) dx, x2 + 4x + 3
5 cos x + 5 sin x + 3 dx, 8) − 1/2 3 cos2 x + 6 cos x − 4 sin x cos x − 3 sin x + 3
8 cos x − 11 sin x − 2 9) − 2 dx, 13 cos2 x + 9 sin x cos x + 24 cos x + 11 + 7 sin x
11 cos x − 32 sin x + 29 dx 17 cos2 x − 19 sin x cos x + 48 cos x + 31 − 21 sin x 10)

7

Вариант 15


1 1) −3e3x + 14 √ − 10(1 + 4x2 )−1 dx, 9 − 49x2

2) (12 + 22x + 40x2 )e−8x dx, 3) 20 sin(5x)ecos(5x) dx,

x2 − 24x − 84 15x2 − 24x − 1 4) dx, 5) 1/2 dx, − 3)(x + 4)2 (x − 1)(x2 − 8x + 17)
(x
√ 12 + 11x − 3x3 + 8x2 √ 6) 2 −x2 − 2xdx, 7) dx, 5 − x2 + 4x
11 cos x + 6 sin x + 9 8) 2 dx,
(5 cos x + 3)(sin x + 1 + cos x) 7 cos x + 15 dx, 9) −
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 33 cos x − 8 sin x + 43 dx 15 cos2 x + 3 sin x cos x + 20 cos x + 5 sin x + 5 10)

Вариант 16


1 1) 20e5x + 4 √ + 2 sin xdx, 1 − 16x2

1 3) −14 √ 2) (7 − 9x + 6x2 ) ln(5x)dx, dx, 1 − 49x2 arcsin(7x)

11x2 − 8x − 37 7x − 23 dx, 5) −2 dx, 4) −2 (1 + x)(x − 4)(x − 3) (1 + x)(x2 + 8x + 25)

√ 12x3 − 110x2 + 287x − 149 √ 6) 2 6x + x2 dx, 7) dx, x2 − 10x + 26
3 cos x − sin x + 7 dx, 8) 1/2 4 cos2 x − 3 sin x cos x + 6 cos x − 2 sin x + 2
3 cos x + 2 sin x + 1 dx, 9) 3
cos2 x + 4 sin x cos x − 4 cos x − 5 + 5 sin x −45 cos x + 10 sin x − 23 dx 16 cos2 x + 13 sin x cos x + 40 cos x + 24 + 15 sin x 10) 2

8

Вариант 17

Вариант 19


1 1 1) −10(1 + 4x2 )−1 + 3 + 2 √ dx, x x

earctg(3x) 2) (−6 + 2x − 3x2 ) ln(8x)dx, 3) 24 dx, 1 + 9x2

3x2 + 17x + 30 5x2 + 26x − 13 4) −2 dx, 5) dx, 2 (x − 1)(x + 4)2

(−1 + 3x)(x − 4x + 5) √ 6x3 + 20x2 + 20x + 7 √ dx, 6) 2 35 − 2x − x2 dx, 7) −x2 − 2x
−9 cos x + 4 sin x − 7 dx, 8) − 3
(5 cos x + 3)(sin x − 1 − cos x) 3 cos x + 7 sin x − 1 dx, 9) −
cos2 x + 3 sin x cos x − 3 cos x + 4 sin x − 4 −21 cos x + 28 sin x − 43 dx −3 cos2 x + 15 sin x cos x − 20 cos x − 17 + 17 sin x

Вариант 18

−2

10)

Вариант 20

−


1 1 1) 3 + 2 cos(2x) − 35 √ dx, 2 x 9 − 49x

earccos(2x) 2) (−1 − 2x) arctg(3x)dx, 3) 8 √ dx, 1 − 4x2

5x2 − 6x − 2 3x2 + 35x + 87 dx, dx, 5) −9/2 4) − 1)(x + 4)2 (x − 1)(x2 − 2x + 10)
(x
√ 67x2 + 15x3 − 35x + 4 √ 6) 2 −5 − x2 + 6xdx, 7) dx, −6x − x2
15 cos x + 5 sin x + 3 dx, 8) − 1/2 −3 cos2 x − 6 cos x + 4 sin x cos x + 3 sin x − 3
7 cos x + 13 sin x + 3 9) − dx,
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 4 cos x + 3 sin x − 5 dx − cos2 x + 3 sin x cos x − 5 cos x + 4 sin x − 4


1 1 1) 2 − 24(1 + 36x2 )−1 − 2 √ dx, 1 − 4x2
x
1 2) (1 + 2x) cos(4x)dx, 3) −18 dx, (1 + 9x2 ) arctg(3x)

1+x −34 − 6x + 7x2 4) −16 dx, 5) 3 dx, (3 + x)(x − 1)(x − 5) (3 + 2x)(10 + 2x + x2 )

√ 15x3 − 83x2 + 112x − 19 √ 6) 2 x2 − 8x − 20dx, 7) dx, x2 − 6x + 8
cos x + 3 sin x + 7 8) − 1/2 dx, 3 cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3
9 sin x + 23 + 23 cos x dx, 9) − 2 13 cos2 x + 9 sin x cos x + 24 cos x + 11 + 7 sin x
9 + 7 sin x dx cos2 x + 3 sin x cos x + 5 cos x + 4 sin x + 4

10)

10)


1 1) 4e−4x − 8 cos(4x) + √ dx, x

2) (27 − 21x − 35x2 )e−5x dx, 3) 12 cos(6x)esin(6x) dx,

4x2 − 20x + 7 11x2 + 20x − 9 4) 2 dx, 5) − dx, 2
(x + 2)(x − 4)(x − 5)
(1 + 3x)(x + 8x + 17) √ 15x3 + 129x2 + 289x + 45 √ 6) 2 x2 − 4x + 53dx, 7) dx, x2 + 10x + 26
20 cos x + 7 sin x + 16 8) dx,
(5 cos x + 3)(sin x + 1 + cos x) −13 cos x + 17 sin x − 23 dx, 9) −
cos2 x + 3 sin x cos x − 3 cos x + 4 sin x − 4 −5 cos x + 3 sin x − 8 dx −5 cos2 x − 10 cos x + sin x − 5

10

10) 2

9

Вариант 21

−2


1 1) 15 √ + 20e5x + 20 sin(4x)dx, 1 − 9x2

earctg(5x) 2) (63 − 31x − 63x2 )e−7x dx, 3) −30 dx, 1 + 25x2

x2 + 33x + 126 25x2 − 38x + 16 4) dx, 5) 2 dx, 2 − 2)(x + 5)2 − 8x + 25)
(x
(−3 + 2x)(x √ −76x + 10x2 + 12x3 + 46 √ 6) 2 12 − x2 − 4xdx, 7) dx, 8 − 2x − x2
cos x + 2 sin x − 4 dx, 8) −
−3 cos2 x − 6 cos x + 4 sin x cos x + 3 sin x − 3 5 cos x + 5 sin x + 9 dx, 9) −
11 cos2 x + 2 sin x cos x + 18 cos x + sin x + 7 5 sin x + 14 dx 7(cos x)2 + 11 sin x cos x + 20 cos x + 13 + 13 sin x 10)

Вариант 22

Вариант 23


1 1) −2e−2x + 4 √ − 6 sin(3x)dx, 1 − 4x2

1 2) (3 + 3x) arccos(4x)dx, 3) 6 dx, 2

(1 + 9x ) arcctg x(3x) 2x2 + x − 59 17x2 − 20x + 16 4) dx, 5) dx, 2 − 2)(x + 5)2
(x
(x − 1)(x −3 8x + 20) √ −58x − 12x − 98x2 + 9 √ 6) 2 −16 − x2 + 10xdx, 7) dx, −9 − x2 − 10x
−2 cos x + sin x − 3 dx, 8) − −3 cos2 x − 6 cos x + 4 sin x cos x + 3 sin x − 3
− cos x + 6 sin x − 5 dx, 9)
cos2 x + 2 sin x cos x − 2 cos x + 3 sin x − 3 20 cos x + sin x + 13 dx −5 cos2 x + 5 sin x cos x − 15 cos x − 10 + 6 sin x 10)

Вариант 24

−


1 1) 10 cos(5x) + 5 √ + 3x−1 dx, x

1 dx, 2) (12 − 21x − 27x2 )e−9x dx, 3) −10  arcctg x(5x)(1 + 25x2 )

7x2 − 12x − 24 2x2 − 17x + 18 dx, 5) 2 dx, 4) 2 2
(x + 2)(x − 3)(x − 6)
(x − 2)(x + 4x + 8) √ −6x3 − 30x2 − 44x − 14 √ 6) 2 x2 − 10x + 21dx, 7) dx, x2 + 4x + 3
9 cos x + 2 sin x + 4 8) − dx, 3 cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3
5 sin x + 29 + 29 cos x dx, 9) 19
cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 −3 cos x + 10 sin x + 7 dx −15 cos2 x + 3 sin x cos x − 20 cos x + 5 sin x − 5 10)


1 1) 8 cos(4x) − 4e4x + 3 dx, x

cos(4x) 2) (−1 + 4x + 4x2 ) ln(8x)dx, 3) 8  dx, sin(4x)

5x2 + 4x + 1 4x2 − 11x + 2 dx, 5) 1/2 dx, 4) − 2 2 (x − 1)(x − 8x + 17)
√(x − 3)(x − 4)
3 + 17x2 + 17x − 124 −3x √ 6) 2 x2 − 6x − 7dx, 7) dx, x2 − 10x + 24
7 cos x + 8 sin x + 1 8) dx, (5
cos x + 3)(sin x − 1 − cos x) −8 cos x + 7 sin x − 4 dx, 9) − 2
(5 cos x + 3)(sin x + 2 + 2 cos x) 12 cos x + sin x + 10 dx 16 cos2 x + 13 sin x cos x + 40 cos x + 24 + 15 sin x

12

10) 4

11

Вариант 25

Вариант 27


1 1) −2ex + 45(9 + 25x2 )−1 + √ dx, x

1 2) (−42 + 36x + 81x2 )e−9x dx, 3) −72 √ dx, 1 − 81x2 arccos(9x)

−9 − 11x + x2 71x2 − 8x − 25 4) − dx, 5) − dx, 2 2
(x − 2)(1 + x)
(1 + 3x)(x − 4x + 13) √ −39 + 11x + 37x2 + 9x3 √ 6) 2 39 − x2 + 10xdx, 7) dx, −8 − 6x − x2
5 cos x + 2 sin x + 3 8) − 3 dx,
(5 cos x + 3)(sin x + 1 + cos x) 30 cos x + 11 sin x + 34 dx, 9) − 2
16 cos2 x + 13 sin x cos x + 32 cos x + 11 sin x + 16 −33 cos x + 14 sin x − 27 dx −57 cos2 x − 108 cos x + sin x cos x − sin x − 51

−3

Вариант 28

10) 3


1 1 1) 2 √ + 20 √ − 3e3x dx, x 1 − 25x2

1 2) (6 + 8x + 5x2 ) ln(9x)dx, 3) −5  dx, √ arcsin(5x) 1 − 25x2

15x2 − 6x − 8 13 + 19x + 6x2 dx, 5) − 4) − dx, 2 2
(x − 2)(3 + x)
(−1 + 2x)(x − 6x + 10) √ 15x2 + 10x − 15x3 + 2 √ dx, 6) 2 9 − x2 − 8xdx, 7) −x2 + 2x
2 cos x + sin x + 3 dx, 8) 3 3 cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3
2 cos x − sin x − 2 9) − 2 dx,
16 cos2 x + 13 sin x cos x + 32 cos x + 11 sin x + 16 6 cos x + 28 sin x − 17 dx 10 cos2 x − 10 sin x cos x + 26 cos x + 16 − 11 sin x −

Вариант 26

10)


1 1) 15e5x − 6(4 + 9x2 )−1 − 3 √ dx, 1 − x2

1 dx, 3) −8  2) (6 + 5x − 9x2 ) ln(2x)dx, arcctg x(2x)(1 + 4x2 )

55 − 22x + 27x2 x2 + 4x − 15 dx, 5) − dx, 4) 2 (1 + x)(x − 2)(x − 3) + 3x)(13 + 6x + x2 )
√
(−2 12x3 − 58x2 + 59x − 3 √ 6) 2 x2 − 6x − 27dx, 7) dx, x2 − 6x + 8
−11 cos x + 7 sin x − 5 8) 1/2 dx,
3 cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3 7 cos x + 9 sin x + 12 dx, 9) − 2
11 cos2 x + 2 sin x cos x + 18 cos x + sin x + 7 8 cos x + 7 sin x + 1 dx −10 cos2 x + 10 sin x cos x − 26 cos x + 11 sin x − 16 10)

14


1 1) −3 √ − cos x − 6(1 + 4x2 )−1 dx, x

earctg(9x) 2) (x − 2) cos(4x)dx, 3) −54 dx, 1 + 81x2

3x2 − 25x + 66 5x2 + 16x − 49 4) dx, 5) dx, + 2x)(x2 − 8x + 17)
(−1
(3√+ x)(x − 4)(x − 5) 3 6x − 30x2 + 6x + 95 √ 6) 2 x2 + 4x + 3dx, 7) dx, x2 − 8x + 17
3 cos x + 2 sin x + 6 8) dx,
(5 cos x + 4)(sin x + 1 + cos x) 37 cos x + 17 sin x + 41 dx, 9)
(5 cos x + 4)(sin x + 3 + 3 cos x) 23 cos x − 36 sin x + 41 dx 17 cos2 x − 19 sin x cos x + 48 cos x + 31 − 21 sin x 10)

13

Вариант 29

Вариант 31


1 1) −35(1 + 49x2 )−1 + 3 √ − 4 sin(2x)dx, x

1 2) (8 + 9x + 9x2 ) ln(3x)dx, 3) −27  dx, √ arccos(9x) 1 − 81x2

23x2 − 62x − 31 x2 + 23x + 58 dx, 5) 4) − dx, 2 2
(x − 2)(x + 4)
(x − 3)(x − 4x + 13) √ −6x2 − 9x + 3x3 − 8 √ dx, 6) 2 63 − 2x − x2 dx, 7) −x2 + 4x
−20 cos x + 7 sin x − 16 dx, 8)
(5 cos x + 3)(sin x − 1 − cos x) −17 cos x + 8 sin x − 13 dx, 9) −
19 cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 4 cos x + 3 sin x + 8 dx 3 cos2 x + 15 sin x cos x + 20 cos x + 17 + 17 sin x −2

Вариант 32

10)


1 1) −5 √ + 25 sin(5x) + 2 cos(2x)dx, x

1 2) (−3 − x) arcctg x(4x)dx, 3) −15  dx, arctg(5x)(1 + 25x2 )

−34 − 14x + 11x2 x + 11 dx, 5) 1/2 dx, 4) 3 2 (1 + x)(10 + 2x + x2 )
(x − 1)(x + 5)
√ −4 + 23x2 + 20x + 3x3 √ dx, 6) 2 32 − x2 − 4xdx, 7) −16 − x2 − 10x
−7 cos x + 4 sin x − 2 dx, 8)
3 cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3 27 cos x + 2 sin x + 17 9) − dx,
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 −12 cos x + 5 sin x − 11 dx − cos2 x + 3 sin x cos x − 5 cos x + 4 sin x − 4

Вариант 30

10)


1 1 1) 4 − 16 √ + 2 sin(2x)dx, 1 − 16x2
x
1 2) (−2 + 3x) arccos(2x)dx, 3) 28 √ dx, 1 − 49x2 arcsin(7x)

7x2 − 2x − 14 7x2 − 20x − 27 dx, 5) −2 dx, 4) − 2 2 (x + 2)(x − 2x + 10)
√(x − 5)(−9 + x )
2 − 15x3 + 14 −4x − 17x √ 6) 2 x2 + 4x + 13dx, 7) dx, 2 + 2x + x2
− cos x + 4 sin x − 7 8) dx,
(5 cos x + 3)(sin x − 1 − cos x) −6 cos x + 17 sin x + 4 dx, 9) −
19 cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 −10 cos x + 3 sin x + 7 dx 3 cos2 x + 9 sin x cos x + 13 cos x + 10 + 10 sin x 10)

16


1 1 1) 4 − 3 sin x + 7 √ dx, x 1 − 49x2

earctg(3x) 2) (36 − 24x − 15x2 )e−5x dx, 3) −12 dx, 1 + 9x2

13x − 50 17x2 − 46x + 11 4) dx, 5) −2/3 dx, (x − 1)(x2 − 8x + 25)

(1√+ x)(x − 2)(x − 6) 3 15x + 129x2 + 294x + 69 √ 6) 2 −55 + 6x + x2 dx, 7) dx, x2 + 10x + 26
5 cos x + 7 sin x + 1 8) dx, (5 cos x + 4)(sin x − 1 − cos x)
cos x + sin x dx, 9) − 4 cos2 x + 3 sin x cos x − 3 cos x + 4 sin x − 4
−19 cos x + 4 sin x − 13 dx 21 cos2 x + 27 sin x cos x + 60 cos x + 29 sin x + 39 10)

15

Вариант 33
1 1) 3 sin x + 30(4 + 25x2 )−1 + √ dx, x

cos(8x) 2) (11 − 2x − 12x2 )e−2x dx, 3) 16  dx, sin(8x)

39 + 20x + x2 8 + 2x + 3x2 dx, 5) 3 dx, 4) 2 2
(x − 3)(3 + x)
(1 + x)(10 + 2x + x ) √ −117x − 83x2 − 15x3 − 33 √ 6) 2 −24 − x2 − 10xdx, 7) dx, −8 − 6x − x2
7 cos x + 2 sin x + 6 8) 3 dx,
(5 cos x + 4)(sin x + 1 + cos x) 3 sin x − 5 − 5 cos x dx, 9)
cos2 x + 3 sin x cos x − 3 cos x + 4 sin x − 4 −2 cos x + 27 sin x − 15 dx −5 cos2 x − 10 cos x + sin x − 5 10)

Вариант 34

−


1 1) 4 + 2 sin(2x) − 16(1 + 16x2 )−1 dx,
x
2) (6 + 7x − 9x2 ) ln(6x)dx, 3) 20 sin(5x)ecos(5x) dx,

x2 − 26x − 15 5x2 − 7x − 7 4) − dx, 5) −2 dx, (−1 + 2x)(x2 − 2x + 10)
(3 + x)(x − 1)(x − 6)
√ −9x3 + 85x2 − 228x + 116 √ 6) 2 x2 − 10x + 29dx, 7) dx, x2 − 10x + 26
17 cos x − 3 sin x + 3 dx, 8)
(5 cos x + 3)(sin x + 1 + cos x) 3 cos x + 14 sin x − 1 dx, 9) −
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 14 cos x − 6 sin x + 5 dx 8 cos2 x − 4 sin x cos x + 15 cos x + 7 − 3 sin x 10)

17

Вариант 35


1 1) −6 sin(3x) + 12 cos(3x) + 4 dx,

x 1 2) (x − 1) arcsin xdx, 3) 14 dx, (1 + 49x2 ) arcctg x(7x)

2x + 43 19x2 + 56x + 49 4) dx, 5) dx, − 3)(x + 4)2 (2 + 3x)(x2 + 8x + 25)
(x
√ 112x − 12x3 + 34x2 + 39 √ 6) 2 60 − x2 − 4xdx, 7) dx, 12 − x2 + 4x
5 cos x − 4 sin x − 1 8) − 2 dx,
(5 cos x + 3)(sin x + 1 + cos x) 5 cos x − 8 sin x + 9 dx, 9) −
cos2 x + 2 sin x cos x − 2 cos x + 3 sin x − 3 cos x + 7 sin x − 1 dx 4 cos2 x + 3 sin x cos x + 8 cos x + 4 + sin x 10) 2

Вариант 36

−


1 1) −28(4 + 49x2 )−1 − 8 sin(4x) − 35 √ dx, 2
9 − 49x
1 dx, 2) (−23 + 23x − 30x2 )e5x dx, 3) 5  √ arccos(5x) 1 − 25x2

66 + 78x + 25x2 x2 − 4x + 16 dx, 5) dx, 4) 3 2 2
(x − 5)(x − 4)
(x + 2)(18 + 6x + x ) √ −3x3 − 3x2 − 5x √ 6) 2 −63 + 2x + x2 dx, 7) dx, 2 + 2x + x2
5 cos x + 1 − sin x 8) 2 dx,
(5 cos x + 4) cos x 5 cos x − 18 sin x + 15 dx, 9) −
cos2 x + 4 sin x cos x − 4 cos x − 5 + 5 sin x cos x + 3 sin x − 8 dx 4 cos2 x + 5 cos x − sin x + 1 10)

18

Вариант 37

Вариант 39


1 1) 3 cos(3x) + 2e−x + 4 √ dx, 1 − x2

earccos(8x) 2) (−43 + 22x − 72x2 )e8x dx, 3) −48 √ dx, 1 − 64x2

15x2 + 16x − 44 5x2 + 22x − 47 dx, dx, 5) − 4) − 2 2 20)
√(x − 3)(x + 5)
(3 + 2x)(x3 − 8x + −87x + 12x + 44x2 − 33 √ dx, 6) 2 −12 − x2 − 8xdx, 7) 12 − x2 − 4x
−11 sin x + 23 + 23 cos x dx, 8) − 1/2 4 cos2 x − 3 sin x cos x + 6 cos x − 2 sin x + 2
11 cos x − 8 sin x + 3 9) − dx,
11 cos2 x + 2 sin x cos x + 18 cos x + sin x + 7 7 cos x − sin x + 14 dx 8 cos2 x + 4 sin x cos x + 15 cos x + 7 + 3 sin x

Вариант 38

−2

10) 2

Вариант 40

−


1 1) −3(1 + x2 )−1 − 12e4x − 4 √ dx, x

cos(8x) 2) (3 + 8x + 9x2 ) ln(2x)dx, 3) 16  dx, sin(8x)

9x2 − 28x + 24 −3 − 21x + 2x2 dx, 5) −2 dx, 4) − (x − 3)(1 + x)2 (x − 2)(x2 − 4x + 8)

√ −28x + 6x3 + 18x2 + 6 √ 6) 2 −x2 + 10xdx, 7) dx, 5 − x2 − 4x
4 cos x − 8 sin x + 5 8) dx,
4 cos2 x − 3 sin x cos x + 6 cos x − 2 sin x + 2 15 cos x − 4 sin x + 5 dx, 9) −
cos2 x + 2 sin x cos x + 2 cos x + sin x + 1 22 cos x − 3 sin x + 9 dx cos2 x − 3 sin x cos x + 5 cos x − 4 sin x + 4


1) 10e−2x + 50(4 + 25x2 )−1 + 8 sin(2x)dx,

1 dx, 3) −2  2) (1 − 8x + 2x2 ) ln(4x)dx, arctg(2x)(1 + 4x2 )

5x2 + 16x − 40 2x2 − 11x + 30 dx, 5) − dx, 4) 2 (x + 2)(x − 3)(x − 6) (−1 + 2x)(x2 + 4x + 8)

√ 15x3 − 46x2 + 15x + 13 √ 6) 2 x2 − 4x − 32dx, 7) dx, x2 − 4x + 3
11 cos x − 7 sin x + 19 8) 1/2 dx,
4 cos2 x − 3 sin x cos x + 6 cos x − 2 sin x + 2 cos x + sin x − 3 dx, 9) − 3
cos2 x + 3 sin x cos x + 3 cos x + 2 + 2 sin x 10 cos x + 3 sin x + 14 dx 15 cos2 x − 3 sin x cos x + 20 cos x − 5 sin x + 5

10)

10)


1 1) −4 √ − 4 cos x + 20(1 + 16x2 )−1 dx, x

1 2) −(−3 − 3x) arctg(5x)dx, 3) 20 dx, (1 + 25x2 ) arcctg x(5x)

3x2 − 12x + 5 3x2 − x + 12 4) −3 dx, 5) −2 dx, (1 + 2x)(x2 − 6x + 10)
√ (1 + x)(x − 4)(x − 3)
−9x3 + 73x2 − 128x − 28 √ dx, 6) 2 x2 − 10x + 24dx, 7) x2 − 10x + 24
7 cos x + 2 sin x + 6 dx, 8) − 3 (5 cos x + 4)(sin x + 1 + cos x)
13 cos x − 5 sin x + 5 dx, 9) cos
2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 3 cos x − 14 sin x + 8 dx 14 cos2 x − 2 sin x cos x + 26 cos x − 3 sin x + 12

20

10)

19

Вариант 41

−


1 1 1) −3 sin x + 4 − 3 √ dx, x x

sin(9x) dx, 2) −(x + 2) arcsin xdx, 3) −54 cos(9x)

4x2 − 2x − 79 25x2 − 12x + 12 4) − dx, dx, 5) −2 2 2 (−2 + 3x)(x − 8x + 20)

√(x − 3)(x + 4) 110x + 15x3 − 98x2 + 5 √ 6) 2 −x2 − 10xdx, 7) dx, −12 − x2 + 8x
13 cos x + 3 8) − dx, (5 cos x + 3)(sin x + 1 + cos x)
43 cos x + 15 sin x + 47 dx, 9) (5
cos x + 4)(sin x + 3 + 3 cos x) 5 cos x − 12 sin x + 27 dx 3 cos2 x − 11 sin x cos x + 16 cos x − 13 sin x + 13 10)

Вариант 42

−2


1 1 1) 5 + 3 √ − 4 cos xdx, x x

earcsin(4x) 2) (−2 + 45x − 81x2 )e9x dx, 3) −8 √ dx, 1 − 16x2

−10 − 2x + 5x2 x2 − 6x + 11 dx, 5) −1/2 dx, 4) −2 (1 + x)(2 + 2x + x2 )
√ (1 + x)(x − 2)(x − 3)
3 + 108x2 − 197x + 60 −15x √ 6) 2 x2 + 8x − 9dx, 7) dx, x2 − 8x + 15
−3 + 7 sin x 8) dx,
(5 cos x + 4)(sin x − 1 − cos x) −2 cos x + 3 sin x dx, 9) −
cos2 x + 4 sin x cos x − 4 cos x − 5 + 5 sin x 4 cos x + 9 sin x + 1 dx −15 cos2 x − 26 cos x + sin x − 11 10)

21

Вариант 43


1 1 1) 15 √ + 4 − 12 cos(3x)dx, x 9 − 25x2

2) (4 − 8x + x2 ) ln(5x)dx, 3) −24 sin(6x)ecos(6x) dx,

1 − 6x + x2 7x2 + 4x + 7 4) −2 dx, 5) 2 dx, 2 2
√ (x − 3)(1 + x)
(x − 1)(x 2 + 4x + 13) 3 −25 − 29x − 68x − 3x √ 6) 2 −3 − x2 + 4xdx, 7) dx, −21 − x2 − 10x
−5 cos x + 15 sin x + 3 8) − 1/2 dx, 4 cos2 x + 3 sin x cos x + 6 cos x + 2 + 2 sin x
−15 cos x + 2 sin x − 7 dx, 9) −
cos2 x + 2 sin x cos x + 2 cos x + sin x + 1 9 cos x + sin x + 8 dx 4 cos2 x + 8 sin x cos x + 15 cos x + 11 + 9 sin x 10) 2

Вариант 44


1 1 1) 16 √ − 5 sin x + 2 dx, x
9 − 16x2
cos(4x) dx, 2) (1 − 2x) cos xdx, 3) 8  sin(4x)

22 − 34x + 25x2 x2 − 7x + 40 dx, 5) 2 dx, 4) 2
(3 + x)(x − 2)(x − 4)
(−1 + 2x)(10 + 2x + x ) √ 12x3 + 78x2 + 104x − 27 √ 6) 2 x2 − 10x − 11dx, 7) dx, x2 + 8x + 15
3 sin x + 1 + cos x 8) dx,
3 cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3 14 sin x + 19 + 19 cos x dx, 9)
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 33 cos x − 16 sin x + 35 dx 12 cos2 x − 21 sin x cos x + 40 cos x − 23 sin x + 28 10)

22

Вариант 47


1 1 1) 5 √ − 3 √ + 5e−x dx, x 1 − x2

1 2) −(2 − x) sin(5x)dx, 3) −24  dx, arctg(8x)(1 + 64x2 )

6 + 18x + 13x2 6x2 + 37x + 31 dx, 5) − dx, 4) 2 2
(x − 3)(x + 4)
(1 + 3x)(2 + 2x + x ) √ 31 + 83x + 53x2 + 9x3 √ 6) 2 −21 − x2 − 10xdx, 7) dx, −8 − 6x − x2
8 cos x + sin x + 10 dx, 8) 4
cos2 x + 3 sin x cos x + 6 cos x + 2 + 2 sin x 3 sin x + 7 + 7 cos x 9) − 3 dx, cos2 x + 3 sin x cos x + 3 cos x + 2 + 2 sin x
57 cos x + 22 sin x + 35 dx 25 cos2 x − 15 sin x cos x + 60 cos x + 35 − 17 sin x

Вариант 45
1 1 1) −4 cos(4x) + 3 + 4 √ dx, x x

1 2) (84 + 17x − 45x2 )e9x dx, 3) −36  dx, √ arccos(9x) 1 − 81x2

11x2 − 14x − 23 4x2 + 40x + 89 dx, 5) 2/3 4) dx, 2 (x − 1)(x2 + 8x + 17)
(x − 3)(x + 4)
√ −69 + 67x2 + 68x + 9x3 √ dx, 6) 2 −x2 − 4xdx, 7) −21 − x2 − 10x
9 cos x + 17 sin x + 1 dx, 8) − 1/2 4 cos2 x − 3 sin x cos x + 6 cos x − 2 sin x + 2
2 cos x − 9 sin x − 8 9) 2 dx,
13 cos2 x + 9 sin x cos x + 24 cos x + 11 + 7 sin x sin x + 3 dx cos2 x + 3 sin x cos x + 5 cos x + 4 sin x + 4


1 1) 8 sin(2x) − 18 √ + 14(4 + 49x2 )−1 dx, 1 − 36x2

1 dx, 2) (−14 − 42x + 36x2 )e−4x dx, 3) −64 (1 + 64x2 ) arcctg x(8x)

3x2 − 8x − 19 x2 + 2x + 1 4) −2 dx, 5) 15 dx, (3 + x)(x − 1)(x − 5) (−1 + 2x)(x2 − 4x + 13)

√ −5 + 26x + 26x2 + 6x3 √ 6) 2 x2 + 8x + 32dx, 7) dx, 10 + 6x + x2
6 cos x + sin x + 5 8) − 3 dx,
(5 cos x + 4)(sin x + 1 + cos x) 17 cos x + 3 sin x + 15 dx, 9) −
cos2 x + 3 sin x cos x + 3 cos x + 2 + 2 sin x 2 sin x − 3 dx 4(cos x)2 + 5 cos x + sin x + 1

Вариант 46

10)

10)

−2

Вариант 48

10)


1 1) 3 cos x − √ + 12e4x dx, x

sin(5x) 3) 15  dx, 2) (−7 + 7x + x2 ) ln(5x)dx, cos(5x)

3x2 + 7x + 3 3x2 − 10x − 9 dx, 5) 2 dx, 4) −2 2 + 4x + 5)
√ (3 + x)(x − 1)(x − 5)
(−1 + 2x)(x 22x + 50x2 + 12x3 − 35 √ 6) 2 x2 − 6x + 10dx, 7) dx, 8 + 6x + x2
9 cos x + 3 sin x + 7 dx, 8) − 3/2 4 cos2 x + 3 sin x cos x + 6 cos x + 2 + 2 sin x
9 cos x + 3 sin x + 8 9) − 2 dx, cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3
27 cos x + 10 sin x + 1 dx 20 cos2 x − 5 sin x cos x + 40 cos x + 20 − 7 sin x

24

10) 2

23

Вариант 49

Вариант 51


1 1) −14(1 + 49x2 )−1 + 5 cos x + 5 √ dx, x

earcctg x(3x) 2) −4e−2x (2 + 2x + x2 )dx, 3) −24 dx, 1 + 9x2

3x2 + 7x + 1 3x2 − 4x − 3 4) − dx, 5) 2 dx, 2 2 5)
√(x − 3)(x + 4)
(1 + x)(x3 + 2x + 125x + 3x + 35x2 + 129 √ dx, 6) 2 −x2 − 4xdx, 7) −24 − x2 − 10x
19 cos x + 3 sin x + 15 dx, 8) − 1/2 4 cos2 x + 3 sin x cos x + 6 cos x + 2 + 2 sin x
7 cos x − 14 sin x − 1 dx, 9) − 2
13 cos2 x + 9 sin x cos x + 24 cos x + 11 + 7 sin x 21 cos x − 20 sin x + 31 dx 12 cos2 x − 21 sin x cos x + 40 cos x − 23 sin x + 28 −

Вариант 52

10)


1 1 1) 4 − 15 sin(5x) + 3 √ dx, x
x
1 2) 6(1 − x + x2 ) ln(4x)dx, 3) −18  dx, arcctg x(6x)(1 + 36x2 )

3x2 − 16x + 1 x2 − 6x − 11 dx, 5) 2 dx, 4) − 2 2
(x − 1)(1 + x)
(x − 3)(x + 2x + 5) √ 43x + 9x3 + 73x2 + 12 √ dx, 6) 2 8 − x2 + 2xdx, 7) −9 − x2 − 10x
19 cos x − 3 sin x + 15 dx, 8) 1/2 4 cos2 x − 3 sin x cos x + 6 cos x − 2 sin x + 2
6 sin x + 1 + cos x 9) dx,
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 12 cos x − 19 sin x + 26 dx 10 cos2 x − 10 sin x cos x + 26 cos x + 16 − 11 sin x

Вариант 50

10)


1 1) 75(9 + 25x2 )−1 + 4 + 10e−2x dx, x

earctg(5x) dx, 2) 4(2 − 2x + x2 ) ln(3x)dx, 3) 10 1 + 25x2

3x2 − 3x − 20 25x2 − 18x − 18 4) dx, 5) 2 dx, 2 2
(x − 6)(x − 1)
(−3 + 2x)(x − 6x + 18) √ −66x2 − 123x − 34 − 9x3 √ 6) 2 x2 − 2x + 17dx, 7) dx, x2 + 8x + 15
10 cos x − 3 sin x + 5 8) − dx,
(5 cos x + 4)(sin x + 1 + cos x) 7 cos x − 7 sin x + 10 dx, 9) − 2
cos2 x + 4 sin x cos x − 4 cos x − 5 + 5 sin x 7 cos x + 12 sin x + 25 dx 11 cos2 x + 3 sin x cos x + 16 cos x + 5 sin x + 5 10) 2

26


1 1 1) 3 √ + 3 √ + 8e−4x dx, x 1 − 9x2

sin(3x) dx, 2) (2 + 3x) arcctg x(5x)dx, 3) −12  cos(3x)

−6 − 2x + 3x2 x2 − 4x + 14 dx, 5) − dx, 4) −2 + x)(2 + 2x + x2 )
√ (3 + x)(x − 2)(x − 4)
(1 3 − 25x2 + 61x − 40 3x √ dx, 6) 2 x2 + 8x − 48dx, 7) x2 − 6x + 10
(5 cos x + 3 + 3 sin x) sin x 8) − 1/2 dx, (5 cos2 x + 8 cos x + 3) cos x
−7 sin x + 3 + 3 cos x dx, 9) −
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 8 cos x − 9 sin x + 22 dx 11 cos2 x − 23 sin x cos x + 36 cos x − 25 sin x + 25 10) 2

25

Вариант 55


1 1 1) 100(16 + 25x2 )−1 + 6 √ + 3 √ dx, x 1 − 9x
2
1 2) (1 − 7x + 9x2 ) ln(3x)dx, 3) −4  dx, √ arccos(4x) 1 − 16x2

−26 − 2x + 13x2 x2 − 9x − 4 dx, 5) 4) dx, 2 2
(x − 1)(1 + x)
(1 + 2x)(10 + 6x + x ) √ −37x − 6x3 + 42x2 − 7 √ dx, 6) 2 15 − x2 − 2xdx, 7) −7 − x2 + 8x
25 cos x − 5 sin x + 13 dx, 8) 1/2
3 cos2 x + 6 cos x − 4 sin x cos x − 3 sin x + 3 9 cos x + 3 sin x − 1 9) − dx,
cos2 x + 3 sin x cos x + 3 cos x + 2 + 2 sin x 21 cos x − 20 sin x − 5 dx 3 cos2 x + 11 sin x cos x + 16 cos x + 13 sin x + 13

Вариант 53

Вариант 56

10)

10)


1 1) 4 √ + 15 sin(3x) + 60(16 + 25x2 )−1 dx, 1 − x2

1 2) (−3 − 3x) arcctg x(3x)dx, 3) −8 dx, (1 + 16x2 ) arctg(4x)

2x2 + 23x + 93 7x2 − 42x + 66 4) − dx, 5) dx, 2 2
√(x − 2)(x + 5)
(x − 2)(x 2− 6x + 18) 3 −27 − 26x − 58x − 3x √ 6) 2 −x2 − 8xdx, 7) dx, −12 − x2 − 8x
8 cos x − sin x + 10 dx, 8) −
4 cos2 x − 3 sin x cos x + 6 cos x − 2 sin x + 2 5 cos x − 5 sin x + 2 dx, 9) − 4
13 cos2 x + 9 sin x cos x + 24 cos x + 11 + 7 sin x 6 cos x − 28 sin x − 17 dx 10 cos2 x + 10 sin x cos x + 26 cos x + 11 sin x + 16


1 1) −12 sin(3x) + 2 + 9 cos(3x)dx, x

2) (−3 − x) arctg(3x)dx, 3) −16 cos(8x)esin(8x) dx,

7x2 − 34x + 31 x2 − 3 4) − dx, 5) −15 dx, (1 + 3x)(x2 − 4x + 13)
√(1 + x)(x − 3)(x − 5)
54 + 147x + 85x2 + 15x3 √ 6) 2 x2 − 6x + 5dx, 7) dx, 10 + 6x + x2
10 cos x + 5 sin x + 11 dx, 8) 3
cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3 42 cos x + 7 sin x + 38 dx, 9) − 2 16 cos2 x + 13 sin x cos x + 32 cos x + 11 sin x + 16
17 cos x − 18 sin x + 35 dx 24 cos2 x + 3 sin x cos x + 40 cos x + 16 + sin x

10)

−


1 1) −4 √ − 12 sin(4x) − 16 cos(4x)dx, x

1 dx, 2) (48 + 72x − 32x2 )e−8x dx, 3) 8  arcctg x(4x)(1 + 16x2 )

5x2 − 10x + 14 x2 − 6x + 4 dx, 5) 2 dx, 4) 3 2 2
(x − 3)(x − 4)
(x − 3)(x + 4x + 8) √ −1 − x + x2 + 3x3 √ 6) 2 x2 − 10x + 16dx, 7) dx, 2 − 2x + x2
11 cos x − 2 sin x + 8 8) − dx, 4 cos2 x − 3 sin x cos x + 6 cos x − 2 sin x + 2
13 cos x − 7 sin x + 9 dx, 9)
19 cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 17 cos x + 54 sin x − 29 dx 23 cos2 x + 36 cos x − 11 sin x cos x − 13 sin x + 13

28

10)

Вариант 54

27

Вариант 57

Вариант 59


1 1) −16 sin(4x) + 5 √ − 84(16 + 49x2 )−1 dx, 1 − 25x2

1 2) (−3 − x) cos(5x)dx, 3) −6  dx, √ arccos(2x) 1 − 4x2

9x2 + 24x − 1 7x2 − 3x − 4 dx, 5) −2 4) − dx, 2 (3 + x)(x2 + 2x + 5)
(x − 2)(1 + x)
√ −62 + 23x2 + 81x − 9x3 √ dx, 6) 2 −15 − x2 + 8xdx, 7) 15 − x2 + 2x
13 cos x + 2 sin x + 14 dx, 8) (5
cos x + 4)(sin x + 1 + cos x) 10 cos x − 11 sin x + 2 dx, 9) − 2 (5 cos x + 3)(sin x + 2 + 2 cos x)
18 cos x + 4 sin x + 13 dx 16 cos2 x − 12 sin x cos x + 39 cos x − 13 sin x + 23 10)


1) 8 sin(2x) − 56(4 + 49x2 )−1 − 20e−5x dx,

earcctg x(5x) dx, 2) (−22 + 2x + 6x2 )e−2x dx, 3) 40 1 + 25x2

6x2 + 41x + 61 7x2 + 15x + 36 4) dx, 5) −2 dx, − 1)(x + 5)2 (3 + 2x)(x2 − 6x + 18)
(x
√ −25x + 3x3 − 16x2 + 9 √ dx, 6) 2 27 − 6x − x2 dx, 7) −x2 + 8x
25 cos x + 3 + 3 sin x dx, 8) 1/2
(5 cos x + 3) cos x cos x + 2 sin x − 3 dx, 9) − 3
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 17 cos x − 4 sin x + 27 dx 40 cos2 x − 5 sin x cos x + 72 cos x − 7 sin x + 32 −3

Вариант 60

10)

Вариант 58

10)

−


1 1) −2 √ + 15 cos(3x) − 15 sin(5x)dx, x

1 2) (10 + 26x + 6x2 )e6x dx, 3) −8 √ dx, 1 − 4x2 arcsin(2x)

3x2 + 4x − 36 3x2 + 16x − 13 4) − dx, 5) − dx, 2 2
√(x − 6)(x − 4)
(1 3+ x)(x 2− 8x + 17) −6x + 22x − 31x + 10 √ 6) 2 x2 − 10xdx, 7) dx, x2 − 4x + 5
13 cos x + 8 8) dx,
5 cos2 x − 5 sin x cos x + 9 cos x + 4 − 4 sin x cos x + sin x − 3 dx, 9) 2
cos2 x + 3 sin x cos x + 3 cos x + 2 + 2 sin x 3 cos x − 38 sin x + 25 dx 20 cos2 x − 5 sin x cos x + 40 cos x + 20 − 7 sin x

−

30


1 1 1) 5 − 5ex + 4 √ dx, 1 − 4x2

x 3) 36 sin(6x)ecos(6x) dx, 2) (3 + 4x + 3x2 ) ln(8x)dx,

2x2 + x − 13 6 + 10x + x2 4) − dx, 5) − dx, + x)(2 + 2x + x2 )
√(1 + x)(x − 2)(x − 3)
(3 6x3 + 20x2 + 18x + 8 √ 6) 2 x2 + 8x − 20dx, 7) dx, x2 + 2x
10 cos x + 7 sin x + 2 8) dx,
5 cos2 x − 5 sin x cos x + 8 cos x + 3 − 3 sin x 13 cos x + 21 sin x + 21 9) dx, 11 cos2 x + 2 sin x cos x + 18 cos x + sin x + 7
2 cos x + 19 sin x + 19 dx sin x + 10 cos x + 5 + 5 cos2 x 10)

29

Вариант 61

−2


1 1 1 1) −4 √ + 4 + 25 √ dx, x x 1 − 25x2

1 2) (7 − 7x + 5x2 ) ln(3x)dx, 3) −56 √ dx, 1 − 49x2 arccos(7x)

8x2 − 5x + 7 2 − 32x + 11x2 4) dx, 5) −2 dx, − 3)(1 + x)2 (−1 + 2x)(10 + 2x + x2 )
(x
√ 6x3 − 13x + 4 √ 6) 2 8 − 2x − x2 dx, 7) dx, −x2 − 2x
4 cos x − 2 sin x + 1 8) 2 dx,
4 cos2 x + 3 sin x cos x + 6 cos x + 2 + 2 sin x 3 cos x + 19 sin x + 11 dx, 9) −
19 cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 3 cos x + 14 sin x + 1 dx 24 cos2 x + 3 sin x cos x + 40 cos x + 16 + sin x 10)

Вариант 62


1 1) 4e−2x − 5 sin(5x) + √ dx, x

2) (1 + 3x) arcctg x(4x)dx, 3) 32 sin(4x)ecos(4x) dx,

7x2 − 30x − 9 19x2 − 70x + 63 4) − dx, 5) dx, 2 2
√(x − 5)(−9 + x )
(x −33)(x −2 2x + 5) −6x + 58x − 159x + 75 √ 6) 2 6x + x2 dx, 7) dx, x2 − 10x + 26
−15 cos x + 5 sin x − 17 8) − 1/2 dx, −4 cos2 x + 3 sin x cos x − 6 cos x + 2 sin x − 2
7 sin x − 1 − cos x dx, 9)
cos2 x + 4 sin x cos x − 4 cos x − 5 + 5 sin x 23 cos x + 14 sin x + 13 dx − cos2 x + 7 sin x cos x − 12 cos x − 11 + 9 sin x 10)

31

Вариант 63

− 26


1) 15e5x + 28(4 + 49x2 )−1 − 15 cos(5x)dx,

cos(5x) dx, 2) (−15 + 9x − 27x2 )e3x dx, 3) −20 sin(5x)

4x2 + 15x + 3 7x2 − 16x − 9 4) − dx, dx, 5) −3/2 2 2 (x − 1)(x + 4x + 13)
√(x − 2)(x + 5)
8 − 36x2 + 6x + 6x3 √ 6) 2 20 − x2 + 8xdx, 7) dx, −7 − x2 + 8x
−13 cos x + 6 sin x − 12 8) dx, −4
cos2 x + 3 sin x cos x − 6 cos x + 2 sin x − 2 −19 cos x + sin x − 13 dx, 9) − 2
16 cos2 x + 13 sin x cos x + 32 cos x + 11 sin x + 16 sin x + 2 dx 11 cos2 x + 7 sin x cos x + 20 cos x + 9 + 9 sin x 10)

Вариант 64

−2


1 1 1) −7 √ + 16 sin(4x) + 2 dx, x
1 − 49x2
1 2) (−3 + 9x + 8x2 ) ln(8x)dx, 3) 16  dx, √ arccos(8x) 1 − 64x2

5x2 − 28x + 20 37x2 − 78x + 54 4) − dx, 5) −2/3 dx, (x − 1)(x2 − 6x + 18)
(x + 2)(x − 4)(x − 6)
√ 17 − 29x − 41x2 − 9x3 √ 6) 2 x2 − 10x + 41dx, 7) dx, 8 + 6x + x2
3 sin x + 1 + cos x dx, 8) −
3 cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3 −34 cos x − 29 + 3 sin x dx, 9) − 2
25 cos2 x + 40 cos x + 16 −5 cos x + 6 sin x − 8 dx −2 cos2 x + 6 sin x cos x − 10 cos x + 7 sin x − 8 10)

32

Вариант 65

Вариант 67

−


1 1 1) −6(1 + 4x2 )−1 + 3 √ + 5 dx, x x

1 2) (3 − 7x + 5x2 ) ln(4x)dx, 3) 16 dx, (1 + 64x2 ) arctg(8x)

19 + 37x + 8x2 3x2 − 4x − 12 4) dx, 5) −3 dx, − 2)(3 + x)2 (−3 + 2x)(x2 − 6x + 18)
(x
√ −31x − 9x3 − 58x2 + 1 √ 6) 2 −5 − 6x − x2 dx, 7) dx, −7 − x2 − 8x
−13 cos x + sin x − 5 dx, 8) −
3 cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3 −7 cos x + 15 sin x + 3 dx, 9) − 2
(5 cos x + 3)(sin x + 2 + 2 cos x) 17 cos x + 66 sin x + 67 dx 28 cos2 x + 29 sin x cos x + 72 cos x + 44 + 31 sin x

10)

Вариант 68

10)


1 1 1) 2 + 20(4 + 25x2 )−1 − 14 √ dx, 2
x
16 − 49x 1 2) (−2 − 2x) cos xdx, 3) −36 √ dx, 1 − 81x2 arccos(9x)

55 + 22x + 3x2 47x2 + 34x − 17 4) dx, 5) −1/3 dx, − 1)(3 + x)2 (1 + x)(x2 + 2x + 5)
(x
√ 34 + 64x2 + 99x + 9x3 √ 6) 2 −7 − x2 − 8xdx, 7) dx, −12 − x2 − 8x
−4 cos x + 3 sin x + 1 8) dx, 3
cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3 26 cos x + 11 sin x + 22 dx, 9) − 2
16 cos2 x + 13 sin x cos x + 32 cos x + 11 sin x + 16 17 cos x + 6 sin x + 11 dx 3 cos2 x + 15 sin x cos x + 20 cos x + 17 + 17 sin x −2

Вариант 66

10)


1 1 1) 3 + 4 √ − 5 cos xdx, x
x
cos(4x) 2) (x − 1) cos xdx, 3) −8  dx, sin(4x)

11x2 + 12x − 12 x2 − 8x + 3 dx, 5) −2 dx, 4) −2 2 (2 + 3x)(x2 + 8x + 20)
√ (x − 1)(−9 + x )
9x2 − 13x + 9x3 − 8 √ 6) 2 x2 − 2x + 65dx, 7) dx, x2 + 2x
13 cos x + 4 sin x + 5 8) dx,
−4 cos2 x + 3 sin x cos x − 6 cos x + 2 sin x − 2 33 cos x + 12 sin x + 35 9) dx,
19 cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 23 cos x + 26 sin x + 37 dx cos2 x + 7 sin x cos x + 12 cos x + 11 + 9 sin x

−2

34


1 1 1) 5 − 5 √ + 3e−3x dx, x
x
1 2) (10 + 14x + 6x2 )ex dx, 3) 24 √ dx, 1 − 16x2 arcsin(4x)

x − 11 45x2 − 4x − 32 4) dx, 5) dx, 2
(−1 + 3x)(x + 4x + 8)
(3 + x)(x − 4) √ 15 + 39x + 35x2 + 15x3 √ 6) 2 x2 − 2xdx, 7) dx, 2 + 2x + x2
7 cos x + 2 sin x + 8 8) − 2 dx, (5 cos x + 4)(sin x + 1 + cos x)
−3 cos x + 3 sin x − 4 dx, 9) 4 cos
2 x + 3 sin x cos x − 3 cos x + 4 sin x − 4 −15 cos x + 44 sin x − 41 dx −25 cos2 x + 15 sin x cos x − 60 cos x − 35 + 17 sin x 10)

33

Вариант 69

−3


1 1 1) 8e4x + 3 − 2 √ dx, x 1 − 4x2

1 2) (−58 + 56x + 32x2 )e8x dx, 3) −30 √ dx, 1 − 25x2 arcsin(5x)

6x2 + 5x + 9 31x2 − 8x − 36 4) dx, 5) −1/2 dx, 2 2 (x − 1)(x − 8x + 20)
(x − 1)(1 + x)
√ −10x − 6x3 + 34x2 − 43 √ 6) 2 11 − x2 + 10xdx, 7) dx, −12 − x2 + 8x
− cos x + 4 sin x − 7 8) dx,
(5 cos x + 3)(sin x − 1 − cos x) 19 cos x + 9 sin x + 17 dx, 9) 2 (5
cos x + 3)(sin x + 2 + 2 cos x) 13 cos x + sin x + 12 dx 16 cos2 x + 12 sin x cos x + 39 cos x + 23 + 13 sin x 10)

Вариант 70

Вариант 71


1 1) 5 + 4e−x + 8 cos(4x)dx,
x
2) (−3 + 3x) arccos(3x)dx, 3) −4 cos(2x)esin(2x) dx,

x(6x + 37) 61 − 50x + 17x2 4) − dx, dx, 5) − 2 + 6x + x2 )
√(x − 2)(x + 5)
(−3 + 2x)(13 148x + 12x3 + 94x2 − 66 √ 6) 2 27 − 6x − x2 dx, 7) dx, −24 − x2 − 10x
sin x − 4 8) − dx,
(5 cos x + 3)(sin x − 1 − cos x) 7 sin x + 3 dx, 9) 2
(5 cos x + 4)(sin x + 3 + 3 cos x) 6 cos x − 31 sin x + 32 dx 10 cos2 x − 10 sin x cos x + 26 cos x + 16 − 11 sin x 10)

Вариант 72

−


1 1 1) −2(1 + 4x2 )−1 − 3 √ − 21 √ dx, x 16
− 49x2
cos(4x) dx, 2) (−21 + 40x − 42x2 )e6x dx, 3) 16  sin(4x)

−3 − 7x + x2 2x2 + 5x − 38 dx, 5) −4 dx, 4) − (−2 + 3x)(10 + 6x + x2 )
√(3 + x)(x − 2)(x − 4)
3 + 3x + 7x2 + 3x3 √ 6) 2 x2 − 10x + 16dx, 7) dx, 2 + 2x + x2
cos x − 3 sin x dx, 8) −
4 cos2 x + 3 sin x cos x + 6 cos x + 2 + 2 sin x 2 cos x + sin x + 1 9) − 9 dx,
25 cos2 x + 40 cos x + 16 24 cos x + 26 sin x + 37 dx 10 cos2 x + 10 sin x cos x + 26 cos x + 11 sin x + 16 10)


1 1) 8 sin(2x) + 3 cos(3x) − 25 √ dx, 16 −
25x2
sin(3x) dx, 2) (−6 + 9x − 7x2 ) ln(8x)dx, 3) 6

cos(3x) 2 x2 + 10x − 47 7x + 10x − 18 4) − dx, 5) −2 dx, (1 + 2x)(x2 − 8x + 17)
√(x + 2)(x − 1)(x − 5)
2 − 102x − 98 − 3x3 −31x √ 6) 2 x2 − 2x − 48dx, 7) dx, x2 + 10x + 26
−22 cos x + 3 sin x − 6 dx, 8) − (5 cos x + 3)(sin x + 1 + cos x)
− cos x + 10 sin x − 9 dx, 9)
cos2 x + 2 sin x cos x − 2 cos x + 3 sin x − 3 − cos x + 2 sin x − 11 dx 11 cos2 x + 7 sin x cos x + 20 cos x + 9 + 9 sin x

36

10) 3

35

Вариант 73

Вариант 75

−


1 1 1) 6 cos(2x) − 2 √ − 4 √ dx, x 1 − x2

2) (−30 + 20x − 21x2 )e−7x dx, 3) −6 sin(3x)ecos(3x) dx,

6x2 + 3x + 1 10 + 8x + 3x2 4) − dx, 5) − dx, 2 2
√(x − 3)(1 + x)
(12+ x)(2 − 2x3 + x ) + 9x + 9x + 1 19x √ 6) 2 −24 − x2 + 10xdx, 7) dx, −x2 − 2x
12 cos x + 5 sin x + 8 8) dx,
(5 cos x + 3)(sin x + 1 + cos x) cos x + 8 sin x + 3 dx, 9) −
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 15 cos x + 16 sin x − 7 dx −7 cos2 x + 11 sin x cos x − 20 cos x − 13 + 13 sin x

10)

−

Вариант 76

10)


1 1) −12 cos(3x) + 3 √ + 2e−x dx, x

2) (−2 + 7x − 7x2 ) ln(2x)dx, 3) 54 sin(9x)ecos(9x) dx,

7x2 + 30x + 10 7x2 − 18x − 22 4) dx, 5) −3 dx, − 2)(x + 5)2 (x − 3)(x2 − 2x + 10)
(x
√ 83x2 + 15x3 + 39x + 10 √ 6) 2 24 − x2 + 10xdx, 7) dx, −6x − x2
10 cos x + 3 sin x + 5 8) dx,
5 cos2 x − 5 sin x cos x + 9 cos x + 4 − 4 sin x 7 cos x + 7 sin x − 3 dx, 9) −
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 −13 cos x + 9 sin x − 17 dx −28 cos2 x + 29 sin x cos x − 72 cos x − 44 + 31 sin x

Вариант 74

10) 4


1 1) 20 √ − 10e5x − 60(16 + 25x2 )−1 dx, 9 − 25x2

1 3) −20  dx, 2) (−8 − 9x − 8x2 ) ln(9x)dx, √ arccos(5x) 1 − 25x2

x2 + 32x − 8 x2 − 8x + 9 dx, 5) − dx, 4) −2 (1 + x)(x − 2)(x − 3) (1 + x)(x2 − 4x + 8)

√ 114x + 70x2 + 12x3 + 57 √ 6) 2 x2 + 10x + 61dx, 7) dx, 8 + 6x + x2
−3 cos x + 11 sin x − 5 8) 1/2 dx, −4 cos2 x + 3 sin x cos x − 6 cos x + 2 sin x − 2
6 sin x + 25 + 25 cos x dx, 9) 3
19 cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 −21 cos x + 2 sin x − 15 dx −4 cos2 x − 8 cos x + 3 sin x cos x + sin x − 4

−2

38


1 1) 2 √ − 60(9 + 25x2 )−1 − 3 cos xdx, x

earcctg x(4x) dx, 2) (x − 2) cos xdx, 3) 8 2

1 + 216x 2x2 − 11x + 33 7x − 18x + 24 4) − dx, 5) dx, 2 2
(x − 4)(−9 + x )
(x − 1)(x − 6x + 18) √ 92x2 − 137x − 73 − 12x3 √ dx, 6) 2 x2 − 8x − 9dx, 7) x2 − 10x + 24
11 cos x + 4 sin x + 13 dx, 8)
(5 cos x + 3)(sin x + 1 + cos x) 7 cos x + 2 sin x − 1 dx, 9) cos
2 x + 2 sin x cos x + 2 cos x + sin x + 1 11 cos x + 21 sin x + 37 dx 40 cos2 x + 5 sin x cos x + 72 cos x + 32 + 7 sin x 10)

37

Вариант 77

Вариант 79


1 1 1) 3 cos(3x) + 21 √ − 3 √ dx, x 9 − 49x2

earcsin(6x) 2) (−1 + 9x + 6x2 ) ln(7x)dx, 3) 24 √ dx, 1 − 36x2

71x2 + 62x + 2 23 + 8x + x2 dx, dx, 5) − 4) −2 2 2
√ (x − 1)(3 + x)
(1 + 3x)(x 3− 2x + 10) −252x − 15x − 131x2 − 53 √ dx, 6) 2 −5 − 6x − x2 dx, 7) −21 − x2 − 10x
−9 cos x + 7 sin x − 2 dx, 8)
4 cos2 x + 3 sin x cos x + 6 cos x + 2 + 2 sin x −25 cos x + 7 sin x − 17 9) dx, (5
cos x + 4)(sin x + 3 + 3 cos x) −19 cos x + 12 sin x − 13 dx 29 cos2 x + 3 sin x cos x + 60 cos x + 5 sin x + 31 −3

−

Вариант 80

10)


1 1) 9(1 + 9x2 )−1 + 5 √ − 2 cos xdx, x

earcctg x(2x) 2) (x − 2) sin xdx, 3) 16 dx, 1 + 4x2

x2 + 3x − 3 −22 + 10x + 17x2 4) 5 dx, 5) dx, 2 (x − 3)(x + 2)2
√
(3 + 2x)(2 + 2x2+ x )3 22 − 42x + 26x + 6x √ 6) 2 35 − 2x − x2 dx, 7) dx, 7 − 6x − x2
−3 cos x + 2 sin x − 1 dx, 8) − 2 (5 cos x + 3)(sin x + 1 + cos x)
5 sin x − 7 − 7 cos x dx, 9)
cos2 x + 2 sin x cos x − 2 cos x + 3 sin x − 3 −43 cos x + 66 sin x − 65 dx 57 cos2 x + 108 cos x + sin x cos x − sin x + 51

Вариант 78

10)


1) 15e−3x − 10 cos(2x) − 6(1 + 36x2 )−1 dx,

1 2) (1 − x) arccos(5x)dx, 3) 24 dx, (1 + 36x2 ) arctg(6x)

4x2 − 15x − 9 5x2 − 36x + 54 4) 2 dx, 5) dx, 2 2
(x − 3)(x − 6x + 18)
(x − 5)(−9 + x ) √ −12x + 18x2 − 12x3 − 8 √ 6) 2 x2 − 4x + 29dx, 7) dx, 2 − 2x + x2
cos x − 4 sin x + 7 8) dx, 5
cos2 x − 5 sin x cos x + 8 cos x + 3 − 3 sin x −2 sin x + 3 + 3 cos x dx, 9) − 4
cos2 x + 3 sin x cos x − 3 cos x + 4 sin x − 4 −4 cos x + 8 sin x − 9 dx −5 cos x + 4 sin x cos x − 5 + 5 sin x 10)

40


1 1) −5e−x − 9 cos(3x) + 4 dx, x

2) (−9 − 12x − 2x2 )ex dx, 3) 16 cos(2x)esin(2x) dx,

x2 + 10x − 35 x2 − 26x + 75 4) dx, 5) − dx, 2
(3 + x)(x − 1)(x − 4)
(x − 3)(x − 8x + 17) √ 15x − 12x2 + 6x3 − 2 √ 6) 2 x2 + 8x − 9dx, 7) dx, 2 − 2x + x2
5 cos x + sin x + 3 8) 3 dx,
(5 cos x + 4)(sin x − 1 − cos x) 37 cos x + 11 sin x + 39 dx, 9) −
19 cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 −41 cos x + 18 sin x − 27 dx 29 cos2 x + 3 sin x cos x + 60 cos x + 5 sin x + 31 10) 3

39

Вариант 81

Вариант 83


1 1) 12 cos(3x) + 3 − 10 sin(2x)dx, x

earcsin(5x) 2) −(x + 2) arctg(4x)dx, 3) −20 √ dx, 1 − 25x2

7x2 + 44x + 49 47x2 − 100x + 40 4) − dx, 5) 1/3 dx, 2 2 (x − 1)(x + 4x + 8)
√(x − 1)(x + 4)
73x + 3x3 + 33x2 + 7 √ dx, 6) 2 −x2 + 8xdx, 7) −9 − x2 − 10x
(−13 cos x + 3 sin x − 3) sin x 8) 1/2 dx, (5 cos2 x + 8 cos x + 3) cos x
5 cos x + 9 sin x − 3 dx, 9) cos
2 x + 4 sin x cos x − 4 cos x − 5 + 5 sin x −2 cos x + 7 sin x + 5 dx cos2 x + 3 sin x cos x + 5 cos x + 4 sin x + 4 −2

10) 2

10)


1) 8 cos(4x) + 15 sin(5x) + 2x−1 dx,

earcsin(6x) dx, 2) e−x (−9 − 13x + 8x2 )dx, 3) 36 √ 1 − 36x2

4 + 17x + 3x2 6 − 26x + 15x2 4) dx, 5) − dx, 2) − 2)(3 + x)2
(x
(−1 + 2x)(2 +32x + x √ −14 + 13x − 3x − 8x2 √ dx, 6) 2 45 − x2 − 4xdx, 7) 5 − x2 − 4x
5 cos x − 8 sin x + 11 dx, 8) −
5 cos2 x − 5 sin x cos x + 8 cos x + 3 − 3 sin x 17 cos x + 16 sin x + 19 dx, 9) −
19 cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 22 cos x − 35 sin x + 39 dx 15 cos2 x − 15 sin x cos x + 39 cos x + 24 − 16 sin x −

Вариант 84

10)

Вариант 82


1 1 1) −10 sin(5x) + 5 − 30 √ dx, x 1 − 36x2

earctg(9x) 3) −72 dx, 2) (−66 − 21x + 27x2 )e9x dx, 1 + 81x2

x2 − 9x + 2 13x2 − 6x + 6 4) −2 dx, 5) dx, 2
√ (x + 2)(x − 4)(x − 6)
(1 3+ x)(x 2 − 6x + 18) + 30x + 51x + 29 6x √ 6) 2 x2 + 10x + 61dx, dx, 7) x2 + 4x + 5
−5 cos x + 7 sin x + 1 8) − dx,
(5 cos x + 3)(sin x + 1 + cos x) 3 cos x + 7 sin x − 5 dx, 9) −
cos2 x + 3 sin x cos x + 3 cos x + 2 + 2 sin x −7 cos x + 12 sin x − 5 dx 15 cos2 x + 3 sin x cos x + 20 cos x + 5 sin x + 5

−3

42


1 1) 3 − 15e5x + 56(4 + 49x2 )−1 dx,

x 1 dx, 2) (−1 + 5x + 2x2 ) ln(3x)dx, 3) 72 (1 + 81x2 ) arcctg x(9x)

x2 + 8x − 11 5x2 − 26x + 37 4) dx, 5) −2 dx, (x − 3)(x2 − 6x + 13)
(1√+ x)(x − 2)(x − 5)
15x3 + 131x2 + 309x + 101 √ 6) 2 x2 + 10x + 89dx, 7) dx, x2 + 10x + 26
13 cos x + 4 sin x + 10 8) dx,
3 cos2 x + 6 cos x + 4 sin x cos x + 3 sin x + 3 11 cos x + sin x + 5 9) dx, cos2 x + 3 sin x cos x + 3 cos x + 2 + 2 sin x
−8 cos x + 2 sin x − 7 dx 8 cos2 x + 4 sin x cos x + 13 cos x + 5 + 5 sin x 10)

41

Вариант 85

Вариант 87


1 1) −12e3x + 20 cos(4x) + 4 √ dx, x

earccos(9x) 2) e−6x (39 − 32x + 42x2 )dx, 3) 36 √ dx, 1 − 81x2

9x2 + 16x + 9 4x2 + 19x + 13 dx, dx, 5) − 4) − 2 2
√(x − 1)(x + 5)
(1 + x)(x3 + 4x 2+ 5) 110x + 6x − 56x − 55 √ dx, 6) 2 −15 − x2 − 8xdx, 7) −16 − x2 + 10x
−6 cos x + 3 sin x − 5 dx, 8) − 3
−3 cos2 x − 6 cos x + 4 sin x cos x + 3 sin x − 3 13 cos x + 5 sin x + 15 9) − dx,
cos2 x + 4 sin x cos x + 4 cos x + 3 sin x + 3 17 cos x + 6 sin x + 11 dx 3 cos2 x + 15 sin x cos x + 20 cos x + 17 + 17 sin x −

−

Вариант 88

10)


1 1 1) 7 √ + (1 + x2 )−1 + 3 dx, x 1 − 49x2

earccos(9x) 2) (6 + 2x − 5x2 ) ln(8x)dx, 3) −18 √ dx, 1 − 81x2

49x2 + 64x − 5 4x2 + 8x − 3 dx, dx, 5) − 4) 2 2
(x − 1)(x + 2)
(3 + 2x)(x + 4x + 13) √ −68x − 12x3 + 62x2 − 2 √ dx, 6) 2 −6x − x2 dx, 7) −8 − x2 + 6x
−11 cos x + 4 sin x − 4 dx, 8)
(5 cos x + 4) cos x 5 cos x + 6 sin x + 9 dx, 9) −
cos2 x + 2 sin x cos x + 2 cos x + sin x + 1 4 cos x + 3 dx −2 cos2 x + 6 sin x cos x − 10 cos x + 7 sin x − 8

Вариант 86

10)


1 1) −10(1 + 4x2 )−1 − 3 √ − 5 cos xdx, x

2) (−6 − 7x + 4x2 ) ln(9x)dx, 3) −36 sin(9x)ecos(9x) dx,

2x2 − 11x + 33 5 + 3x2 4) dx, 5) 2 dx, 2 2
(x − 4)(−9 + x )
(1 + x)(13 + 6x + x ) √ 83x2 + 201x + 84 + 9x3 √ 6) 2 −55 + 6x + x2 dx, 7) dx, x2 + 10x + 24
sin x + 4 8) dx,
(5 cos x + 3)(sin x + 1 + cos x) −10 cos x + 17 sin x − 20 dx, 9) cos
2 x + 4 sin x cos x − 4 cos x − 5 + 5 sin x −2 cos x + 9 sin x − 11 dx −5 cos2 x − 10 cos x + sin x − 5 10)

44


1) −15e3x − 8 sin(2x) − 12 cos(4x)dx,

cos(2x) dx, 2) (−3 − x) cos(5x)dx, 3) −16 sin(2x)

7x − 66 73x2 − 28x − 35 4) − dx, 5) dx, 2
(2 +3 3x)(x 2− 4x + 13)
√(x + 2)(x − 3)(x − 6) 12x − 76x + 99x + 17 √ 6) 2 x2 − 6x − 27dx, 7) dx, x2 − 8x + 15
−7 cos x + 6 sin x dx, 8) 4
cos2 x + 3 sin x cos x + 6 cos x + 2 + 2 sin x 6 sin x + 25 + 25 cos x 9) − 3 dx, 19 cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17
−7 cos x + 8 sin x + 7 dx − cos2 x + 4 cos x + 3 sin x cos x + 5 sin x + 5 10)

43

Вариант 89

Вариант 91


1 1 1) 3 − 21 √ − 3 cos xdx, x 1 − 49x2

earccos(2x) 2) (−1 − 9x + 7x2 ) ln(6x)dx, 3) 4 √ dx, 1 − 4x2

3x2 − 5x − 18 −24 + 17x + 5x2 dx, dx, 5) −2 4) − (x − 3)(3 + x)2 (1 + x)(x2 + 8x + 17)

√ 15x3 + 58x2 + 28x + 4 √ dx, 6) 2 15 − x2 + 2xdx, 7) −x2 − 4x
−2 cos x + 3 sin x + 6 dx, 8) (5
cos x + 3)(sin x + 1 + cos x) 7 cos x + 4 sin x + 8 dx, 9) − 2 cos2 x + 3 sin x cos x + 3 cos x + 2 + 2 sin x
25 cos x + 11 dx 57 cos2 x + 108 cos x + sin x cos x − sin x + 51

10)

−2

Вариант 92

10)


1 1 1) 5 + 12 sin(3x) − 5 √ dx, x x

earccos(6x) 2) (−2 − 2x) cos(3x)dx, 3) 36 √ dx, 1 − 36x2

35x2 + 40x + 84 x2 − 16x − 61 dx, dx, 5) − 4) − 3)(x + 2)2 (3 + 2x)(x2 − 8x + 20)
(x
√ −17 − 34x2 − 33x − 9x3 √ dx, 6) 2 −15 − x2 + 8xdx, 7) −3 − x2 − 4x
− cos x + 7 sin x − 4 dx, 8) − −4 cos2 x + 3 sin x cos x − 6 cos x + 2 sin x − 2
−3 cos x + 7 sin x − 5 9) dx, cos
2 x + 3 sin x cos x − 3 cos x + 4 sin x − 4 14 cos x + 3 sin x + 5 dx sin x + 15(cos x)2 + 26 cos x + 11 −

Вариант 90

10)


1 1) −12 sin(4x) − 12 √ + ex dx, 4 − 9x2

earctg(3x) dx, 2) (−1 − 3x) cos(3x)dx, 3) −12 1 + 9x2

x2 − 11x + 4 3x2 − 4x − 1 4) − dx, 5) −15/2 dx, (x − 1)(x2 − 4x + 13)
√(x + 2)(x − 1)(x − 3)
3 − 56x2 + 150x − 81 6x √ 6) 2 x2 − 10xdx, 7) dx, x2 − 10x + 26
2 cos x + 3 sin x + 1 dx, 8) 3
(5 cos x + 4)(sin x − 1 − cos x) −9 cos x + 7 sin x − 1 dx, 9) −
11 cos2 x + 2 sin x cos x + 18 cos x + sin x + 7 −35 cos x + 12 sin x − 25 dx 40 cos2 x + 5 sin x cos x + 72 cos x + 32 + 7 sin x

−2

46


1 1) 6 √ − 6(1 + 9x2 )−1 + 5 sin(5x)dx, 4 − 9x2

2) e7x (−16 − 57x + 21x2 )dx, 3) −64 sin(8x)ecos(8x) dx,

x2 − 13x + 26 17x2 + 34x − 11 4) − dx, 5) dx, 2
(1 + x)(x − 3)(x − 4)
(3 + x)(x − 6x + 13) √ 12x3 − 14x2 − 5x − 2 √ 6) 2 x2 − 4x + 20dx, 7) dx, x2 − 2x
−4 cos x + 7 sin x − 2 8) dx,
4 cos2 x + 3 sin x cos x + 6 cos x + 2 + 2 sin x −39 cos x + 5 sin x − 31 dx, 9) 19
cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 −7 cos x + 6 sin x − 1 dx cos2 x + 7 sin x cos x + 12 cos x + 11 + 9 sin x 10)

45

Вариант 95


1 1) 20 √ − 8 sin(2x) + 21(9 + 49x2 )−1 dx, 1 − 16x2

cos(3x) dx, 2) −(1 + 2x) arcsin(3x)dx, 3) 9  sin(3x)

29x2 + 20x − 48 17 + 6x + x2 dx, 5) − dx, 4) −2 (x − 1)(3 + x)2 (3 + 2x)(x2 + 4x + 8)

√ −4 + 27x2 − 30x − 3x3 √ 6) 2 −x2 + 8xdx, 7) dx, −9 − x2 + 10x
7 cos x − 4 sin x + 10 8) − dx, 4 cos2 x − 3 sin x cos x + 6 cos x − 2 sin x + 2
35 cos x + 12 sin x + 31 dx, 9)
19 cos2 x + 8 sin x cos x + 36 cos x + 7 sin x + 17 21 cos x + 2 sin x + 27 dx 57 cos2 x + 108 cos x − sin x cos x + sin x + 51

Вариант 93

Вариант 96

10)

10) 3


1 1 1) 5 √ − 2e−x + 2 dx, x x

2) e−4x (−33 − 28x + 32x2 )dx, 3) −12 cos(3x)esin(3x) dx,

−55 − 10x + x2 −2 − 30x + 15x2 4) − dx, 5) 1/2 dx, 2 (x − 1)(10 + 6x + x2 )
√(x − 1)(3 + x)
−84x − 9x3 − 73x2 − 2 √ 6) 2 −7 − x2 − 8xdx, 7) dx, −16 − x2 − 10x
−12 cos x + 5 sin x − 9 8) − dx, (5 cos x + 4)(sin x − 1 − cos x)
37 cos x + 3 sin x + 35 dx, 9) (5 cos x + 4)(sin x + 3 + 3 cos x)
− cos x + 7 sin x + 4 dx 4 cos2 x + 8 sin x cos x + 15 cos x + 11 + 9 sin x


1 1) 3 + 2 sin x − 9 cos(3x)dx,

x earccos(7x) 3) 56 √ dx, 2) (39 − 6x − 12x2 )e−4x dx, 1 − 49x2

11x + 1 −66 − 30x + 23x2 4) − dx, 5) −1/2 dx, (1 + x)(18 + 6x + x2 )
√(x + 2)(x − 1)(x − 5)
−61x − 71x2 − 15x3 + 14 √ 6) 2 x2 + 8x − 20dx, 7) dx, 8 + 6x + x2
5 cos x − 8 sin x + 11 dx, 8) −
5 cos2 x − 5 sin x cos x + 8 cos x + 3 − 3 sin x 3 cos x + 7 sin x + 9 9) 2 dx,
(5 cos x + 3)(sin x + 2 + 2 cos x) 18 cos x − 17 sin x + 29 dx 3 cos2 x − 9 sin x cos x + 13 cos x + 10 − 10 sin x

10) 3

−


1) 5 cos x − 15e3x + 9 sin(3x)dx,

cos(4x) 3) −12  dx, 2) (5 − 5x + 9x2 ) ln(4x)dx, sin(4x)

2 − 2x + x2 2x2 + 7x − 51 dx, 5) −15/2 dx, 4) − (1 + x)(x2 − 6x + 18)
√(1 + x)(x − 3)(x − 6)
−22 − 66x − 38x2 − 6x3 √ 6) 2 x2 − 10x + 26dx, 7) dx, 8 + 6x + x2
11 cos x − 3 sin x + 3 dx, 8) − 1/2 4 cos2 x + 3 sin x cos x + 6 cos x + 2 + 2 sin x
24 cos x + 3 sin x + 22 9) − dx,
11 cos2 x + 2 sin x cos x + 18 cos x + sin x + 7 10 cos x + 14 sin x + 19 dx 10 cos2 x + 10 sin x cos x + 26 cos x + 11 sin x + 16

48

10)

Вариант 94

47

Вариант 97

Вариант 99


1 1) −16 cos(4x) − 60(9 + 16x2 )−1 + 2 √ dx,

x 1 2) e−7x (−39 + 10x + 63x2 )dx, 3) −12  dx, arctg(3x)(1 + 9x2 )

17x2 + 20x + 16 x2 + 13x − 3 dx, 5) − dx, 4) 2 2
(x − 2)(1 + x)
(1 + 2x)(x − 4x + 8) √ 10x − 6x3 + 34x2 − 32 √ dx, 6) 2 21 − x2 − 4xdx, 7) −7 − x2 + 8x
(13 cos x + 3 + 3 sin x) sin x 8) 1/2 dx, 2
(5 cos x + 8 cos x + 3) cos x 6 cos x + 5 sin x + 4 dx, 9) −
cos2 x + 4 sin x cos x − 4 cos x − 5 + 5 sin x −8 cos x + sin x − 1 dx cos2 x + 3 sin x cos x + 5 cos x + 4 sin x + 4

10)

−

−2

Вариант 100

−

10)


1 1) −12 √ + 2 cos x + 4 sin(2x)dx, 1 − 36x2

1 2) (4 − 7x − 2x2 ) ln(7x)dx, 3) −8  dx, arcctg x(8x)(1 + 64x2 )

x2 + 12x − 15 x2 − 15x − 14 dx, 5) dx, 4) − 2 2
(x − 3)(x + 2)
(1 + x)(x − 8x + 17) √ 30 − 53x2 − 5x + 9x3 √ dx, 6) 2 −9 − x2 + 10xdx, 7) 7 − x2 + 6x
−7 sin x + 9 + 9 cos x dx, 8) − 3 cos2 x + 6 cos x − 4 sin x cos x − 3 sin x + 3
−7 sin x + 10 + 10 cos x 9) dx, cos
2 x + 4 sin x cos x − 4 cos x − 5 + 5 sin x 14 cos x + sin x + 12 dx 21 cos2 x + 27 sin x cos x + 60 cos x + 29 sin x + 39


1 1 1) −10e5x + √ + 14 √ dx, 2 x 9 − 49x

1 3) −72 √ 2) (7 − 9x + 5x2 ) ln(4x)dx, dx, 1 − 81x2 arccos(9x)

4 + 8x + 13x2 x2 − 12x + 8 dx, 5) 2 dx, 4) − 2
√(1 + x)(x − 2)(x − 6)
(1 3+ x)(102 + 2x + x ) − 26x + 23x 12x √ 6) 2 x2 − 6x − 7dx, 7) dx, 2 − 2x + x2
−9 cos x + 4 sin x − 7 dx, 8) − 3
(5 cos x + 3)(sin x − 1 − cos x) sin x + 4 + 4 cos x dx, 9) − 3
cos2 x + 2 sin x cos x + 2 cos x + sin x + 1 −81 cos x + 26 sin x − 35 dx 20 cos2 x + 5 sin x cos x + 40 cos x + 7 sin x + 20

10)

−2


1 1) −84(9 + 49x2 )−1 + 4 cos(2x) + 14 √ dx, 9 − 49x2

1 dx, 2) −(2 + 2x) sin(5x)dx, 3) 48 (1 + 64x2 ) arctg(8x)

4x2 − 17x + 10 42 − 14x + 19x2 4) dx, 5) − dx, 2
(x + 2)(x − 4)(x − 3)
(−3 + 2x)(10 + 6x + x ) √ 3x3 − 7x2 − 16x + 21 √ 6) 2 x2 − 6x + 8dx, 7) dx, x2 − 6x + 8
17 cos x − 3 sin x + 3 8) 1/2 dx,
(5 cos x + 3) cos x 1 + cos x dx, 9) − 3
cos2 x + 2 sin x cos x − 2 cos x + 3 sin x − 3 24 cos x + 17 sin x + 31 dx 9 cos2 x + 12 sin x cos x + 26 cos x + 17 + 13 sin x

50

10)

Вариант 98

49

( 4 x )

Ɉɬɜɟɬɵ ɤ ɢɧɞɢɜɢɞɭɚɥɶɧɵɦ ɡɚɞɚɧɢɹɦ ɩɨ ɬɟɦɟ «ɇȿɈɉɊȿȾȿɅȿɇɇɕɃ ɂɇɌȿȽɊȺɅ» ȼɚɪɢɚɧɬ ʋ 1

1), 4 arcsin( 2 x )5 ln( x )4 e 2), ( 3 x 32 x 2x ) ln( 8 x )x ( 1xx 2 ) sin( 7 x ) 4 3), 4 e , 4), 3 ln( x5 ) 5 ln( x1 ) x5

1 5), 4 ln( x 24 x5 )18 arctg( x2 ) ln( x1 ) 3 6), x 22 x  x 22 x xarcsin( 1x ) x 5 7), ( 35 x 23 x ) 21x 210 x 2 arcsin§¨¨  ¸¸· © 2 2¹ x x x 8), ln§¨¨ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg§¨¨ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 6 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· 6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ © ©2¹ ¹ tg§ x ·1 ¹ ¨¨ ¸¸ ©2¹ 2 · § x x 1 x 1 x 10), 6 ln¨¨ tg¨¨§ ·¸¸ 2 tg¨¨§ ¸¸·10 ¸¸2 arctg¨¨§ tg¨¨§ ¸¸· ¸¸·ln§¨¨ tg§¨¨ ¸¸·1 ·¸¸ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 2

1), 4 ln( x )3 cos( x )4 arcsin( 2 x ) 1 1 x 1 2), ln( 19 x 2 ) ( 9 x 254 x ) arcctg ( 3 x )  arctg( 3 x ) 6 18 2 18 3), 6 arcsin( 6 x ) , 4), 3 ln( x3 )2 ln( 1x )2 ln( x1 ) 3 x 3 5), ln( 12 x )2 ln( x 26 x13 )4 arctg¨§  ·¸ ¨ ¸ 2 © 2 2¹ §x 1 x 24 x40 ·¸ 6), x 24 x40 x2 x 24 x40 36 ln¨¨   ¸ 6 ©6 3 ¹ 7), 2 ln( x3 x 26 x8 )( 4 x 2x1 ) x 26 x8 x x x 8), ln§¨¨ tg¨¨§ ¸¸·3 ·¸¸ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 6 x x 9), 4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ¸¸·2 ©2¹ 2 § · x x x 10), ln¨¨ tg§¨¨ ¸¸· 4 tg§¨¨ ·¸¸5 ¸¸3 ln§¨¨ tg§¨¨ ¸¸·1 ·¸¸ © ©2¹ ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 3

7x· 1), 5 cos( 3 x )10 x 5 arcsin§¨¨ ¸¸ © 4 ¹ (6 x ) 2), e ( 94 x7 x 2 ) 1 3), 8 arcctg ( 6 x ) , 4),  3 ln( x2 )3 ln( x5 ) x5 x 5), 2 ln( x 28 x20 )16 arctg§¨¨ 2 ·¸¸3 ln( 1x ) ©2 ¹ x 2 6), 21x 24 x x2 21x 24 x 25 arcsin§¨¨  ¸¸· © 5 5¹

7), ( 3x 23 x ) 3x 24 x arcsin( x2 ) x x x 8), 3 ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸2 ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 4 x x 9), 2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· x © ©2¹ © ©2¹ ¹ ¹ tg§¨¨ ¸¸·2 ©2¹ 2 § · x x x x 10), 4 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·5 ¸¸24 arctg§¨¨ tg§¨¨ ¸¸·2 ·¸¸3 ln§¨¨ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

arcctg( 8 x )

1), 6 x 4 ln( x )2 cos( 4 x ) 1 5 x3 5 x2  4 x ( 60 x 390 x 2144 x ) ln( 6 x ) 9 4 36

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 4

2),

3), 6 e , 4), ln( 3x )3 ln( x3 )2 ln( x5 ) 5), ln( x 24 x5 )4 arctg( x2 )ln( 12 x ) 6), x 210 x16 x5 x 210 x16 9 ln( x5 x 210 x16 ) 7), 2 ln( 3x 106 xx 2 )( 14 x5 x 2 ) 106 xx 2 x x x 8), 3 ln¨¨§ tg§¨¨ ¸¸·3 ·¸¸ln¨¨§ tg§¨¨ ¸¸·1 ·¸¸ln¨¨§ tg§¨¨ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 4 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ tg§ x ·1 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 § · x x 1 x 2 x 10), 6 ln¨¨ tg¨¨§ ·¸¸ 4 tg§¨¨ ¸¸·13 ¸¸12 arctg§¨¨ tg§¨¨ ·¸¸ ·¸¸ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹ © ©2¹ ¹

2

cos( 3 x )2 sin( 3 x )

( 2 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 5

1), 4 e

( x4 ) 1x 1 2), arcsin( x ) §¨¨ 2 xx 2 ·¸¸ 2 2¹ © 3 3), 8 arccos ( 4 x ) , 4), 2 ln( x1 )ln( x4 ) x4 5), ln( x3 )6 ln( x 24 x13 ) x 6), x 210 x x5 x 210 x 25 arcsin¨¨§ 1 ¸¸· ©5 ¹ x 1 7), ( 35 x 24 x ) 15x 22 x 5 arcsin§¨¨  ¸¸· © 4 4¹ x x x 8), 3 ln¨¨§ tg§¨¨ ¸¸·3 ·¸¸3 ln¨¨§ tg§¨¨ ¸¸·2 ·¸¸2 ln¨¨§ tg§¨¨ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 4 ln¨§¨ tg¨§¨ ¸·¸4 ¸·¸ 4 ln¨§¨ tg¨§¨ ¸·¸1 ¸·¸ © ©2¹ ¹ tg§ x ·1 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 · § x x x 1 x 2 10), ln§¨¨ tg§¨¨ ¸¸·2 ·¸¸12 ln¨¨ tg§¨¨ ¸¸· 4 tg¨¨§ ¸¸·13 ¸¸18 arctg¨¨§ tg¨¨§ ¸¸· ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹

2), e

( 7 x )

sin( 2 x )

( 2 x )

( 34 x2 x 2 )

, 4), 2 ln( 3x )2 ln( x2 )3 ln( x6 )

arcsin( 6 x )

1), 8 x 2 e

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 6

3), 8 e

3 x 1 5), 8 ln( 136 xx 2 )32 arctg §¨¨  ¸¸· ln( 32 x ) ©2 2 ¹ 2 6), x 28 x20 x4 x 28 x20 36 ln( x4 x 28 x20 ) 7), ln( x3 x 26 x10 )( 2 x42 x 2 ) x 26 x10 x x x 8), 2 ln¨¨§ tg§¨¨ ¸¸·3 ·¸¸ln¨¨§ tg§¨¨ ¸¸·3 ·¸¸3 ln¨¨§ tg§¨¨ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9), 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ¸¸·1 ©2¹ 2 · § x x x x 10), 4 ln¨¨ tg¨¨§ ¸¸· 4 tg¨¨§ ¸¸·5 ¸¸14 arctg¨¨§ tg§¨¨ ¸¸·2 ·¸¸3 ln¨¨§ tg§¨¨ ¸¸·3 ·¸¸ © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 7

1), 2 arctg ( 2 x )4 ln( x )6 x 1 2 x3 7 x2 2),  5 x ( 24 x 3126 x 2180 x ) ln( 9 x ) 9 4 36 3 3), 8 ln( arcsin( 2 x ) ), 4),  ln( x2 )2 ln( x4 ) x4 x 5), ln( 3x )3 ln( x 26 x18 )14 arctg¨¨§ 1 ·¸¸ ©3 ¹ x 6), x 24 x x2 x 24 x 4 arcsin§¨¨ 1 ¸¸· ©2 ¹ x 7), ( 3 x 2x5 ) x 26 x 2 arcsin§¨¨ 1 ·¸¸ ©3 ¹ x x x 8), 2 ln§¨¨ tg¨¨§ ·¸¸3 ·¸¸ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·ln§¨¨ tg¨¨§ ·¸¸1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 · § x x 1 x x 10), 6 ln¨¨ tg¨¨§ ¸¸· 6 tg§¨¨ ¸¸·18 ¸¸14 arctg §¨¨ tg§¨¨ ¸¸·1 ¸¸·2 ln§¨¨ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹ © ©2¹ ¹ ( 4 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 8

1), 2 ln( x )4 cos( 3 x )e 3 1 x 2), ln( 125 x 2 ) ( 25 x 2150 x1 ) arctg( 5 x ) 10 10 50 3), 2 arctg ( 9 x ) , 4), 2 ln( ( x2 ) ( x1 ) ( x3 ) ) x 3 5), ln( 1x )4 ln( x 26 x13 )10 arctg¨¨§  ¸¸· © 2 2¹ 6), 3 406 xx 2  406 xx 2 x49 ln( x3 406 xx 2 ) 7), 5 ln( 1x 22 xx 2 )( 13 x3 x 2 ) 22 xx 2 x x x 8), ln¨¨§ tg¨¨§ ¸¸·3 ·¸¸3 ln§¨¨ tg¨¨§ ¸¸·3 ·¸¸3 ln§¨¨ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 4 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ 2 ¸¸ © ¹ 2 · § x x x x 10), ln¨¨§ tg¨¨§ ¸¸·3 ·¸¸2 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·5 ¸¸6 arctg §¨¨ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ©2¹ ¹ © ©2¹ ¹ ______________________________________________________

ȼɚɪɢɚɧɬ ʋ 9

4x· 1), 2 cos( 3 x )arcsin¨¨§ ¸¸4 sin( 4 x ) © 3 ¹ ( 9 x ) 2), ( 83 x2 x 2 ) e arcctg( 2 x ) 2 3), 6 e , 4), 3 ln( x1 )5 ln( x4 ) x4 1 5), ln( x 26 x10 )2 arctg( x3 ) ln( x1 ) 3 x 5 6), 16x 210 x x5 16x 210 x 9 arcsin¨¨§  ¸¸· © 3 3¹ x 1 7), ( 3x5 x 2 ) 82 xx 2 4 arcsin§¨¨  ¸¸· © 3 3¹ x x x 8), ln§¨¨ tg¨¨§ ¸¸·2 ·¸¸ln§¨¨ tg¨¨§ ¸¸·1 ·¸¸2 ln§¨¨ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 6 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹ 2 · § x x 1 x x 10), 8 ln¨¨ tg§¨¨ ¸¸· 4 tg¨¨§ ¸¸·8 ¸¸20 arctg¨¨§ tg¨¨§ ¸¸·1 ¸¸·ln§¨¨ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ©2¹ ¹ ©2 © 2 ¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 10

2

5x· 1), arctg§¨¨ ¸¸5 sin( 2 x )cos( 5 x ) © 4 ¹

1 3x 2), ( 12 x 36 x 24 x ) ln( 5 x )x 3 x 4 4 3), 4 ln( arcsin( 8 x ) ), 4), ln( ( 1x ) ( x4 ) ( x3 ) ) 2 1 x 5),  ln( 23 x )6 ln( x 22 x10 )8 arctg §¨¨   ¸¸· 3 © 3 3¹ 6), x 28 x15 x4 x 28 x15 ln( x4 x 28 x15 )

7), 2 ln( x2 x 24 x5 )( 5 x 23 x4 ) x 24 x5 x x x 8), ln§¨¨ tg§¨¨ ·¸¸3 ¸¸·3 ln¨¨§ tg§¨¨ ·¸¸2 ¸¸·ln§¨¨ tg§¨¨ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· ¹ © ©2¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹ 2 § · x x x x 10), 4 ln¨¨ tg§¨¨ ·¸¸ 6 tg§¨¨ ·¸¸10 ¸¸28 arctg §¨¨ tg¨¨§ ·¸¸3 ¸¸·2 ln§¨¨ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

( x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 11

1), 3 e 5 arctg ( 4 x )4 sin( 2 x ) 2 2 1 2),  sin( 3 x ) cos( 3 x ) x cos( 3 x ) 9 3 3 1 5 ln( x4 ) 3), 4 sin( 2 x ) , 4), ln( x3 ) x4 x 3 5), ln( 13 x )8 ln( x 26 x13 )20 arctg§¨¨  ·¸¸ © 2 2¹ x 3 6), 7x 26 x x3 7x 26 x 16 arcsin¨¨§  ·¸¸ © 4 4¹ x 1 7), ( 23 x 22 x ) 12x 24 x arcsin§¨¨  ·¸¸ © 4 2¹

x x x 8), 3 ln¨¨§ tg§¨¨ ·¸¸3 ·¸¸2 ln§¨¨ tg§¨¨ ·¸¸2 ·¸¸ln§¨¨ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 4 x x 9), 6 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ¸¸·1 ©2¹ 2 § · x x x x 10), 2 ln¨¨ tg§¨¨ ·¸¸ 4 tg§¨¨ ·¸¸5 ¸¸16 arctg §¨¨ tg§¨¨ ·¸¸2 ¸¸·3 ln§¨¨ tg§¨¨ ·¸¸2 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 12

5x· 1), 2 arctg §¨¨ ¸¸arcsin( 2 x )8 x © 4 ¹ ( x ) 2), e ( 95 x2 x 2 )

sin( 4 x )

3), 8 e , 4), 2 ln( x4 )2 ln( 1x )ln( x1 ) 5), ln( x 28 x17 )10 arctg( x4 )2 ln( x2 ) 6), x 28 x x4 x 28 x 16 ln( x4 x 28 x ) 7), 5 ln( 1x 22 xx 2 )( 12 x4 x 2 ) 22 xx 2 x x x 8), 3 ln§¨¨ tg§¨¨ ·¸¸3 ·¸¸ln§¨¨ tg§¨¨ ·¸¸2 ·¸¸2 ln§¨¨ tg§¨¨ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ tg§ x ·1 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 3 § x x x · 10), ln¨¨ 6 tg§¨¨ ¸¸· 10tg¨¨§ ¸¸· 13 tg§¨¨ ¸¸· ¸¸ © ©2¹ ©2¹ © 2 ¹¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 13

(4 x ) 4x· 1), 2 e 3 arcsin§ 4 cos( 4 x ) ¨ ¸ ¨ ¸ © 3 ¹ 1 4 x3 2), ( 12 x 318 x 236 x ) ln( 7 x ) x 24 x 9 9 4 3), 6 ln( sin( 6 x ) ), 4), ln( x2 )5 ln( x4 ) x4 3 3 x 5), ln( 12 x )4 ln( 136 xx 2 )14 arctg§¨¨  ·¸¸ 2 ©2 2 ¹ x 3 6), 3 166 xx 2  166 xx 2 x25 arcsin§¨¨  ·¸¸ © 5 5¹ x 7), ( x2 ) 2 x 24 x 3 arcsin¨¨§ 1 ·¸¸ ©2 ¹ x x x 8), 3 ln¨¨§ tg§¨¨ ·¸¸3 ¸¸·2 ln§¨¨ tg§¨¨ ·¸¸3 ¸¸·2 ln§¨¨ tg§¨¨ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 4 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 6 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ §x· tg ¨¨ ¸¸2 ©2¹ 2 · § x x x 1 x 2 10), ln¨¨§ tg§¨¨ ·¸¸3 ¸¸·12 ln¨¨ tg§¨¨ ·¸¸ 4 tg§¨¨ ·¸¸13 ¸¸12 arctg §¨¨ tg§¨¨ ¸¸· ·¸¸ © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 14

1), 4 arctg ( 2 x )3 arcsin( x )2 ln( x ) 1 3 3 2),  sin( 2 x ) cos( 2 x ) sin( 2 x ) x 2 4 2

3), 2 ln( arcctg ( 5 x ) ), 4), 3 ln( 3x )2 ln( x4 )ln( x2 ) 5), 3 ln( ( x2 ) ( 102 xx 2 ) )

6), 242 xx 2  242 xx 2 x25 ln( x1 242 xx 2 ) 7), 4 ln( x2 x 24 x3 )( x 23 x3 ) x 24 x3 x x x 8), ln§¨¨ tg§¨¨ ·¸¸3 ¸¸·2 ln§¨¨ tg§¨¨ ·¸¸2 ¸¸·2 ln§¨¨ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· 4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·2 ¨¨ ¸¸ ©2¹ 2 · § x x x 1 x 10), ln¨¨§ tg§¨¨ ·¸¸3 ¸¸·4 ln¨¨ tg§¨¨ ·¸¸ 4 tg§¨¨ ·¸¸8 ¸¸6 arctg§¨¨ tg§¨¨ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©2 © 2 ¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 15

(3 x ) 7x· 1), e 2 arcsin§¨¨ ¸¸5 arctg ( 2 x ) © 3 ¹ ( 8 x ) 2), ( 24 x5 x 2 ) e cos( 5 x ) 4 3), 4 e , 4), 3 ln( x3 )4 ln( x4 ) x4 1 5), 4 ln( x 28 x17 )24 arctg ( x4 ) ln( x1 ) 2

6), x 22 x  x 22 x xarcsin( 1x ) x 2 7), ( 5x 2x ) 5x 24 x 3 arcsin¨¨§  ·¸¸ © 3 3¹ x x x 8), 3 ln§¨¨ tg§¨¨ ·¸¸2 ¸¸·2 ln§¨¨ tg§¨¨ ¸¸·1 ¸¸·3 ln§¨¨ tg§¨¨ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 6 x 9), 6 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ tg§ x ·1 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 · § x x x x 10), ln¨¨ tg§¨¨ ·¸¸ 6 tg¨¨§ ·¸¸10 ¸¸14 arctg§¨¨ tg§¨¨ ¸¸·3 ¸¸·3 ln§¨¨ tg§¨¨ ·¸¸1 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

(5 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 16

1), 4 e arcsin( 4 x )2 cos( x ) 1 2 x3 9 x2 2),  7 x ( 24 x 354 x 284 x ) ln( 5 x ) 12 3 4 3), 2 ln( arcsin( 7 x ) ), 4), 2 ln( x4 )ln( x3 )3 ln( 1x ) x 4 5), 2 ln( 1x )12 ln( x 28 x25 )40 arctg§¨¨  ·¸¸ © 3 3¹ 6), 3 6 xx 2  6 xx 2 x9 ln( x3 6 xx 2 ) 7), ln( x5 x 210 x26 )( 4 x 25 x4 ) x 210 x26 x x x 8), 2 ln¨¨§ tg§¨¨ ·¸¸3 ¸¸·ln§¨¨ tg§¨¨ ·¸¸1 ¸¸·ln§¨¨ tg§¨¨ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 6 x 9), 4 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹ 2 · § x x 1 x 1 x 10), 12 ln¨¨ tg§¨¨ ·¸¸ 2 tg¨¨§ ·¸¸10 ¸¸16 arctg§¨¨ tg§¨¨ ·¸¸ ¸¸·2 ln¨¨§ tg§¨¨ ·¸¸2 ¸¸· © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 17

7x · 1), 3 ln( x )sin( 2 x )5 arcsin§¨¨ ¸¸ © 3 ¹ 1 1 x 2), ln( 19 x 2 ) ( 18 x18 x 22 ) arctg ( 3 x ) 6 18 3 arccos( 2 x ) 1 5 ln( x1 )2 ln( x4 ) 3), 4 e , 4),  x4 3 1 x 5), ln( x1 )12 ln( x 22 x10 )6 arctg §¨¨   ·¸¸ 2 © 3 3¹ x 3 6), 5x 26 x x3 5x 26 x 4 arcsin¨¨§  ·¸¸ © 2 2¹ x 7), ( 4 x15 x 2 ) 6 xx 2 arcsin¨¨§ 1 ·¸¸ ©3 ¹ x x x 8), 3 ln§¨¨ tg§¨¨ ·¸¸3 ·¸¸ln§¨¨ tg§¨¨ ·¸¸2 ·¸¸2 ln§¨¨ tg§¨¨ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 4 x x 9),  2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§ ·1 ¨ ¸ ¨ ¸ ©2¹ 2 · § x x x 1 1 x 10), 2 ln§¨¨ tg§¨¨ ·¸¸1 ¸¸·8 ln¨¨ tg¨¨§ ·¸¸ 2 tg§¨¨ ·¸¸5 ¸¸12 arctg§¨¨   tg¨¨§ ·¸¸ ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © 2 2 © 2 ¹¹

( 5 x )

( 47 x7 x 2 )

2 sin( 4 x )2 x

( 4 x )

2), e

1), e

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 18

sin( 6 x )

3), 2 e , 4), 3 ln( x4 )2 ln( x5 )3 ln( x2 ) 1 5), 2 ln( x 28 x17 )8 arctg ( x4 ) ln( 13 x ) 3 §x 2 x 24 x53 ·¸ 6), x 24 x53 x2 x 24 x53 49 ln¨¨   ¸ 7 ©7 7 ¹ 7), 2 ln( x5 x 210 x26 )( 5 x 22 x1 ) x 210 x26 x x x 8), 2 ln§¨¨ tg¨¨§ ¸¸·2 ·¸¸3 ln§¨¨ tg¨¨§ ¸¸·1 ·¸¸ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 6 x x 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ¸¸·1 ©2¹ 2 · § x x 1 x 1 x 10), 2 ln¨¨ tg§¨¨ ·¸¸ 2 tg¨¨§ ·¸¸5 ¸¸6 arctg§¨¨ tg¨¨§ ·¸¸ ¸¸·2 ln¨¨§ tg§¨¨ ·¸¸2 ¸¸· © ©2¹ ©2¹ ¹ ©2 © 2 ¹ 2¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 19

1), 5 arctg( 2 x )3 ln( x )4 x x x2 · § 2), ¨ ( 6xx 2 ) ln( 8 x )6  ¸¸ x ¨ 2 3 ¹ © arctg( 3 x ) 4 3), 8 e , 4),  4 ln( x1 )2 ln( x4 ) x4

1 5),  ln( 13 x )ln( x 24 x5 )12 arctg( x2 ) 3 x 1 6), 352 xx 2  352 xx 2 x36 arcsin§¨¨  ·¸¸ © 6 6¹ 7), ( 2 x 25 x5 ) x 22 x 2 arcsin( 1x )

x x x 8), 3 ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸3 ln§¨¨ tg¨¨§ ¸¸·1 ·¸¸3 ln¨¨§ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 6 x x 9),  2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ·¸¸1 ©2¹ 2 · § x x x x 10), 4 ln¨¨ tg¨¨§ ¸¸· 6 tg¨¨§ ¸¸·10 ¸¸22 arctg ¨¨§ tg¨¨§ ¸¸·3 ·¸¸3 ln§¨¨ tg§¨¨ ¸¸·1 ·¸¸ © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

1), 2 ln( x )4 arctg ( 6 x )arcsin( 2 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 20

1 1 1 2), cos( 4 x ) sin( 4 x ) x sin( 4 x ) 8 2 4 3), 6 ln( arctg ( 3 x ) ), 4), ln( 3x )3 ln( x5 )2 ln( x1 ) x 1 3 5), 6 ln( 102 xx 2 )12 arctg §¨¨  ·¸¸ ln( 32 x ) © 3 3¹ 2 6), x 28 x20 x4 x 28 x20 36 ln( x4 x 28 x20 ) 7), ln( x3 x 26 x8 )( 5 x 24 x4 ) x 26 x8 x x x 8), 2 ln¨¨§ tg¨¨§ ¸¸·3 ·¸¸ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸2 ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· 4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·2 ¨¨ ¸¸ ©2¹ 2 § · x x 1 x 1 x 10), 4 ln¨¨ tg¨¨§ ¸¸· 2 tg¨¨§ ¸¸·5 ¸¸2 arctg ¨¨§ tg§¨¨ ¸¸· ·¸¸ln§¨¨ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ©2¹ ¹ ©2 © 2 ¹ 2¹ © ©2¹ ¹

5 cos( 4 x )

(5 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 21

( 7 x )

1), 5 arcsin( 3 x )4 e

( 87 x9 x 2 ) 2), e arctg( 5 x ) 2 3), 6 e , 4),  4 ln( x2 )3 ln( x5 ) x5 x 4 5), 12 ln( x 28 x25 )34 arctg §¨¨  ·¸¸ln( 32 x ) © 3 3¹ x 1 6), 12x 24 x x2 12x 24 x 16 arcsin§¨¨  ·¸¸ © 4 2¹ x 1 7), ( 35 x4 x 2 ) 82 xx 2 3 arcsin§¨¨  ·¸¸ © 3 3¹ x x x 8), 3 ln¨¨§ tg¨¨§ ¸¸·3 ·¸¸3 ln§¨¨ tg¨¨§ ¸¸·2 ·¸¸ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 4 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·3 ¨¨ ¸¸ ©2¹ 2 · § x x 1 x 1 x 10), 6 ln¨¨ tg§¨¨ ·¸¸ 2 tg¨¨§ ·¸¸10 ¸¸6 arctg§¨¨ tg¨¨§ ·¸¸ ¸¸·2 ln¨¨§ tg§¨¨ ·¸¸1 ·¸¸ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹ © ©2¹ ¹

(4 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 22

1), 2 sin( 4 x )e 3 ln( x ) 1 4 x3 2), ( 12 x 318 x 29 x ) ln( 8 x ) x 2x 9 9 3), 4 sin( 4 x ) , 4), ln( x3 )ln( x2 )2 ln( x2 )

1 5), ln( x 28 x17 )16 arctg( x4 ) ln( x1 ) 2 6), x 26 x7 x3 x 26 x7 16 ln( x3 x 26 x7 )

7), 3 ln( x5 x 210 x24 )( 5x 24 x ) x 210 x24 x x x 8), 2 ln§¨¨ tg¨¨§ ¸¸·2 ·¸¸3 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸·2 ln§¨¨ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

x 6 x 9), 2 ln§ tg§ ·2 · 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· ¨ ¨ ¸ ¸ ¨ ¨ ¸ ¸ © ©2¹ ¹ © ©2¹ ¹ tg§ x ·2 ¨¨ ¸¸ ©2¹ 2 · § x x 1 x 1 x 10), 3 ln¨¨ tg§¨¨ ¸¸· 2 tg¨¨§ ¸¸·10 ¸¸6 arctg§¨¨ tg¨¨§ ·¸¸ ¸¸·2 ln¨¨§ tg§¨¨ ·¸¸2 ·¸¸ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹ © ©2¹ ¹

( 2 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 23

1), e 2 arcsin( 2 x )2 cos( 3 x ) ( 12 x48 ) 116 x 2 1 3 2),  ( 192 x96 x 2 ) arccos ( 4 x ) arcsin( 4 x ) 64 64 64 2 3), 2 ln( arcctg ( 3 x ) ), 4), ln( x2 )3 ln( x5 ) x5 x 5), 8 ln( x 28 x20 )34 arctg§¨¨ 2 ·¸¸ln( x1 ) ©2 ¹ x 5 6), 16x 210 x x5 16x 210 x 9 arcsin§¨¨  ·¸¸ © 3 3¹ x 5 7), ( 14 x 2x ) 9x 210 x 5 arcsin§¨¨  ·¸¸ © 4 4¹ x x x 8), ln§¨¨ tg¨¨§ ¸¸·3 ·¸¸ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· 6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· §x· © ©2¹ ¹ © ©2¹ ¹ tg ¨¨ ¸¸1 ©2¹ 2 · § x x x 1 1 x 10), 3 ln§¨¨ tg§¨¨ ·¸¸3 ¸¸·2 ln¨¨ tg¨¨§ ·¸¸ 2 tg§¨¨ ·¸¸5 ¸¸10 arctg§¨¨   tg¨¨§ ·¸¸ ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © 2 2 © 2 ¹¹

1), 2 sin( 5 x )10 x 3 ln( x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 24 ( 9 x )

( 13 x3 x 2 ) 2), e 3), 4 arcctg ( 5 x ) , 4), 2 ln( x3 )ln( x6 )3 ln( x2 ) x 5), 8 ln( x 24 x8 )8 arctg §¨¨ 1 ·¸¸2 ln( x2 ) ©2 ¹ 6), x 210 x21 x5 x 210 x21 4 ln( x5 x 210 x21 ) 7), 5 ln( x2 x 24 x3 )( 2 x 25 x2 ) x 24 x3 x x x 8), ln¨¨§ tg¨¨§ ¸¸·3 ·¸¸ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸3 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·3 ¨¨ 2 ¸¸ © ¹ 2 § x x · x x 10), 2 ln¨¨ 106 tg§¨¨ ·¸¸tg§¨¨ ·¸¸ ¸¸4 arctg§¨¨ tg§¨¨ ¸¸·3 ·¸¸ln§¨¨ tg§¨¨ ·¸¸1 ·¸¸ © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 25

(3 x )

1), 4 x 4 arcsin( 5 x )e 1 5 x3 2), ( 15 x 336 x 254 x ) ln( 9 x ) 2 x 26 x 9 9 2 3), 2 arcsin( 5 x ) , 4), 3 ln( 3x )3 ln( x2 ) 3x 1 5), 4 ln( x 26 x10 )22 arctg( x3 ) ln( 12 x ) 2 x 4 6), 9x 28 x x4 9x 28 x 25 arcsin§¨¨  ·¸¸ © 5 5¹ 7), ( 5 x55 x 2 ) x 22 x 3 arcsin( x1 ) x x x 8), 3 ln§¨¨ tg¨¨§ ¸¸·3 ·¸¸3 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸·3 ln§¨¨ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ tg§ x ·2 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 · § x x x 1 x 2 10), ln¨¨§ tg§¨¨ ·¸¸2 ·¸¸12 ln¨¨ tg§¨¨ ·¸¸ 4 tg¨¨§ ·¸¸13 ¸¸12 arctg§¨¨ tg¨¨§ ·¸¸ ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 26

1), 6 x sin( x )3 arctg ( 2 x ) 1 1 1 cos( 4 x ) sin( 4 x ) x sin( 4 x ) 16 4 2

arctg( 9 x )

2),

3), 6 e , 4), 3 ln( 3x )2 ln( x4 )2 ln( x5 ) 3 5), 2 ln( x 28 x17 )14 arctg ( x4 ) ln( 12 x ) 2

6), x 24 x3 x2 x 24 x3 ln( x2 x 24 x3 ) 7), 2 ln( x4 x 28 x17 )( 2 x 25 x2 ) x 28 x17 x x x 8), 2 ln§¨¨ tg¨¨§ ¸¸·3 ·¸¸2 ln§¨¨ tg¨¨§ ¸¸·3 ·¸¸ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 2 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ ¸¸ ©2¹ 2 · § x x x 1 x 10), ln§¨¨ tg§¨¨ ·¸¸3 ¸¸·4 ln¨¨ tg§¨¨ ·¸¸ 4 tg¨¨§ ·¸¸8 ¸¸4 arctg§¨¨ tg¨¨§ ·¸¸1 ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©2 © 2 ¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 27

5x· 1), 2 e x 3 arctg §¨¨ ¸¸2 x © 3 ¹ ( 9 x ) 2), ( 46 x9 x 2 ) e 1 3), 8 ln( arccos ( 9 x ) ), 4), 3 ln( x2 )4 ln( 1x ) 1x 1 x 2 5), ln( 13 x )12 ln( x 24 x13 )12 arctg§¨¨  ·¸¸ 3 3 3¹ © x 5 6), 39x 210 x x5 39x 210 x 64 arcsin§¨¨  ·¸¸ © 8 8¹ 7), ( 14 x3 x 2 ) 86 xx 2 4 arcsin( 3x ) x x x 8), ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸3 ln§¨¨ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

x 6 x 9), 6 ln¨§¨ tg¨§¨ ¸·¸4 ¸·¸ 2 ln¨§¨ tg¨§¨ ¸·¸2 ¸·¸ © ©2¹ ¹ tg§ x ·2 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 · § x x x 1 x 10), 3 ln¨¨§ tg§¨¨ ·¸¸3 ¸¸·6 ln¨¨ tg¨¨§ ¸¸· 6 tg¨¨§ ¸¸·18 ¸¸8 arctg§¨¨ tg¨¨§ ·¸¸1 ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 28 (5 x ) 3x· 1), 3 e arctg¨§ ¸3 arcsin( x ) ¨ ¸ © 2 ¹ 1 5 x2 2), ( 12 x 310 x 224 x ) ln( 2 x )x 3 6 x 4 4 3), 8 arcctg ( 2 x ) , 4), 3 ln( x3 )2 ln( x2 )3 ln( 1x ) 3 x 5), 4 ln( 136 xx 2 )16 arctg ¨¨§  ¸¸·ln( 23 x ) ©2 2 ¹ 6), x 26 x27 x3 x 26 x27 36 ln( x3 x 26 x27 ) 7), ln( x3 x 26 x8 )( 4 x 2x4 ) x 26 x8 x x x 8), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·3 ln§¨¨ tg¨¨§ ¸¸·1 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·3 ¨ ¸ ¨ ¸ ©2¹ 2 · § x x x 1 x 2 10), 3 ln§¨¨ tg§¨¨ ·¸¸2 ¸¸·12 ln¨¨ tg§¨¨ ·¸¸ 4 tg¨¨§ ·¸¸13 ¸¸14 arctg§¨¨ tg¨¨§ ·¸¸ ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹

1), 10 x 5 cos( 5 x )sin( 2 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 29

3 1 x 1 2),  ln( 116 x 2 ) ( 16 x 296 x ) arcctg ( 4 x )  arctg ( 4 x ) 8 32 8 32 3 ln( x5 )ln( x1 ) 3), 6 arctg ( 5 x ) , 4), x5 x 1 1 5), 3 ln( 102 xx 2 )6 arctg¨¨§  ¸¸· ln( 1x ) © 3 3¹ 2 x 1 6), 32x 24 x x2 32x 24 x 36 arcsin§¨¨  ¸¸· © 6 3¹ x 5 7), ( x3x 2 ) 16x 210 x 3 arcsin¨¨§  ¸¸· © 3 3¹ x x x 8), 3 ln§¨¨ tg¨¨§ ¸¸·3 ¸¸·3 ln§¨¨ tg¨¨§ ¸¸·1 ¸¸·ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 6 9), 4 ln¨§¨ tg¨§¨ ¸·¸4 ¸·¸6 ln¨§¨ tg¨§¨ ¸·¸1 ¸·¸ © ©2¹ ¹ tg§ x ·1 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 · § x x x 1 1 x 10), 3 ln§¨¨ tg§¨¨ ·¸¸1 ¸¸·2 ln¨¨ tg§¨¨ ·¸¸ 2 tg¨¨§ ·¸¸5 ¸¸6 arctg§¨¨   tg¨¨§ ¸¸· ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © 2 2 © 2 ¹¹

2), 3 e

( 5 x )

( 22 xx 2 )

, 4), 2 ln( x2 )ln( x6 )3 ln( 1x )

arctg( 3 x )

1), 4 ln( x )3 cos( x )arcsin( 7 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 30

3), 4 e

x 4 2 5), 6 ln( x 28 x25 )8 arctg§¨¨  ¸¸· ln( x1 ) © 3 3¹ 3 6), 3 556 xx 2  556 xx 2 x64 ln( x3 556 xx 2 )

7), 3 ln( x5 x 210 x26 )( 5 x 22 x4 ) x 210 x26 x x x 8), 3 ln§¨¨ tg¨¨§ ¸¸·3 ¸¸·ln§¨¨ tg¨¨§ ¸¸·3 ¸¸·2 ln§¨¨ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ tg§ x ·1 © ©2¹ ¹ ¨ ¸ ¨ ¸ ©2¹ 2 · · § §x· ¸ ¸14 arctg¨¨ tg¨¨ 2 ¸¸3 ¸¸ ¹ © © ¹ ¹

§ x x x 10), ln§¨¨ tg§¨¨ ·¸¸3 ¸¸·2 ln¨¨ 106 tg¨¨§ ¸¸·tg¨¨§ ·¸¸ © ©2¹ ¹ © ©2¹ ©2¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 31

1), 5 arctg ( 7 x )6 x 2 cos( 2 x ) 1 9 x2 2), ( 12 x 318 x 232 x ) ln( 3 x )x 3 8 x 4 4 3 3 ln( x2 )2 ln( x4 ) 3), 6 arccos ( 9 x ) , 4), x4 x 2 5), ln( x3 )12 ln( x 24 x13 )18 arctg§¨¨  ¸¸· © 3 3¹ x 1 6), 632 xx 2  632 xx 2 x64 arcsin§¨¨  ¸¸· © 8 8¹ x 7), ( 2 x3x 2 ) x 24 x 2 arcsin¨¨§ 1 ¸¸· ©2 ¹ x x x 8), ln§¨¨ tg¨¨§ ¸¸·2 ¸¸·3 ln§¨¨ tg¨¨§ ¸¸·1 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 6 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·3 ¨ ¸ ¨ ¸ ©2¹ 2 · § §x· · · § §x· ¸ ¸14 arctg ¨¨ tg¨¨ 2 ¸¸3 ¸¸2 ln¨¨ tg¨¨ 2 ¸¸1 ¸¸ ¹ © © ¹ ¹ © © ¹ ¹

§ x x 10), ln¨¨ 106 tg§¨¨ ¸¸·tg¨¨§ ¸¸· © ©2¹ ©2¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 32

2

1), 4 ln( x )4 arcsin( 4 x )cos( 2 x ) ( 6 x16 ) 14 x 2 1 3 2),  ( 24 x 232 x ) arccos ( 2 x ) arcsin( 2 x ) 16 16 16 3), 4 ln( arcsin( 7 x ) ), 4), 2 ln( 3x )2 ln( x3 )3 ln( x5 ) 1 x 5), 6 ln( x 22 x10 )4 arctg §¨¨   ·¸¸2 ln( x2 ) © 3 3¹ §x 2 x 24 x13 ¸· 6), x 24 x13 x2 x 24 x13 9 ln¨¨   ¸ 3 ©3 3 ¹ 7), 2 ln( 1x 22 xx 2 )( 44 x5 x 2 ) 22 xx 2 x x x 8), 2 ln§¨¨ tg¨¨§ ¸¸·2 ¸¸·ln§¨¨ tg¨¨§ ¸¸·1 ¸¸·2 ln§¨¨ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· 6 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·3 ¨ ¸ ¨ ¸ ©2¹ · § §x· · §3 1 § x ·· ¸ ¸32 arctg¨¨ 22 tg¨¨ 2 ¸¸ ¸¸ln¨¨ tg¨¨ 2 ¸¸1 ¸¸ ¹ © © ¹¹ © © ¹ ¹

§ x x 10), 8 ln¨¨ 136 tg¨¨§ ¸¸·tg§¨¨ ¸¸· © ©2¹ ©2¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 33

· ¸ ¸ ¹

5x· 1), 3 cos( x )3 arctg¨¨§ ¸¸2 x © 2 ¹ ( 2 x ) 2), e ( 27 x6 x 2 ) 2 3), 4 sin( 8 x ) , 4), 2 ln( 3x ) 3 ln( x3 ) 3x x 1 5), 3 ln( 102 xx 2 )4 arctg¨¨§  ¸¸·3 ln( 1x ) © 3 3¹ 6), 24x 210 x x5 24x 210 x arcsin( x5 ) 7), ( 5 x 24 x1 ) 86 xx 2 2 arcsin( 3x ) x x x 8), 2 ln§¨¨ tg¨¨§ ¸¸·3 ¸¸·2 ln§¨¨ tg¨¨§ ¸¸·3 ¸¸·3 ln§¨¨ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 2 ln¨§¨ tg¨§¨ ¸·¸3 ¸·¸ 2 ln¨§¨ tg¨§¨ ¸·¸1 ¸·¸ © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ 2 ¸¸ © ¹ 2 · § x x 1 x 1 x 10), 8 ln¨¨ tg§¨¨ ¸¸· 2 tg§¨¨ ¸¸·5 ¸¸16 arctg ¨¨§ tg§¨¨ ¸¸· ·¸¸3 ln§¨¨ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ ©2 © 2 ¹ 2¹ © ©2¹ ¹

cos( 5 x )

1), 4 ln( x )cos( 2 x )4 arctg( 4 x ) 1 7 x2 ( 12 x 314 x 224 x ) ln( 6 x )x 3 6 x 4 4

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 34

2),

3), 4 e , 4), 2 ln( 3x )3 ln( x6 )2 ln( x1 ) 5), ln( 12 x )3 ln( x 22 x10 ) §x 5 x 210 x29 6), x 210 x29 x5 x 210 x29 4 ln¨¨   2 ©2 2 7), ln( x5 x 210 x26 )( 3 x 25 x3 ) x 210 x26 x x x 8), 2 ln§¨¨ tg¨¨§ ¸¸·2 ¸¸·2 ln§¨¨ tg¨¨§ ¸¸·1 ¸¸·3 ln§¨¨ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 6 x x 9),  2 ln§ tg¨¨§ ¸¸·4 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· ¨ ¨ x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ¸¸·1 ©2¹ 2 § · x x x x 10), ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·4 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·5 ¸¸8 arctg¨¨§ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © ©2¹ ¹

2

1), 2 cos( 3 x )4 sin( 3 x )4 ln( x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 35

( x4 ) 1x 1 1 2),  arcsin( x ) ¨¨§ x 22 x ¸¸· 4 2 2¹ © 5 3), 2 ln( arcctg ( 7 x ) ), 4), ln( x3 ) ln( x4 ) x4 1 x 4 5), ln( 23 x )3 ln( x 28 x25 )4 arctg§¨¨  ¸¸· 3 3¹ 3 © x 1 6), 60x 24 x x2 60x 24 x 64 arcsin§¨¨  ¸¸· © 8 4¹ x 1 7), ( 24 x 23 x ) 12x 24 x arcsin¨¨§  ¸¸· © 4 2¹

x x x 8), 3 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·2 ln§¨¨ tg¨¨§ ¸¸·1 ¸¸·ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9),  2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ¸¸·1 ©2¹ 2 § x x · x x 10), 2 ln¨¨ 22 tg§¨¨ ¸¸·tg¨¨§ ¸¸· ¸¸6 arctg ¨¨§ tg¨¨§ ¸¸·1 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 36

7x· §7x· 1), 2 arctg ¨¨§ ¸¸2 cos( 4 x )5 arcsin¨¨ ¸¸ © 2 ¹ © 3 ¹ (5 x ) 2), ( 67 x6 x 2 ) e 3), 2 arccos ( 5 x ) , 4), 3 ln( x2 )3 ln( x5 )3 ln( x2 ) x 5), 12 ln( 186 xx 2 )16 arctg ¨¨§ 1 ¸¸·ln( x2 ) ©3 ¹ 6), 632 xx 2  632 xx 2 x64 ln( x1 632 xx 2 ) 7), 2 ln( 1x 22 xx 2 )( x 2x4 ) 22 xx 2 x x x 8), 2 ln§¨¨ tg¨¨§ ¸¸·3 ¸¸·3 ln§¨¨ tg¨¨§ ¸¸·3 ¸¸·ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9), 4 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ¸¸·1 ©2¹ 2 · § x x x x 10), 4 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·5 ¸¸18 arctg¨¨§ tg§¨¨ ¸¸·2 ¸¸·ln¨¨§ tg§¨¨ ¸¸·1 ·¸¸ © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

(4 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 37

1), 3 arctg ( x )3 e 8 x 2), ( 3 x 34 x 23 x ) ln( 2 x )x 32 x 23 x 5 3), 4 sin( 8 x ) , 4),  3 ln( x3 )5 ln( 1x ) 1x x 5), 2 ln( x2 )8 ln( x 24 x8 )8 arctg§¨¨ 1 ¸¸· ©2 ¹ x 6), x 210 x x5 x 210 x 25 arcsin§¨¨ 1 ¸¸· ©5 ¹ x 2 7), ( 22 x 2x ) 5x 24 x 5 arcsin§¨¨  ¸¸· © 3 3¹ x x x 8), 3 ln§¨¨ tg¨¨§ ¸¸·3 ¸¸·ln§¨¨ tg¨¨§ ¸¸·1 ¸¸·3 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 6 9), 4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ §x· tg ¨¨ ¸¸1 ©2¹ 2 § · x x x 1 1 x 10), 3 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸·8 ln¨¨ tg§¨¨ ¸¸· 2 tg§¨¨ ¸¸·5 ¸¸16 arctg ¨¨§   tg§¨¨ ¸¸· ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © 2 2 © 2 ¹¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 38

1), 8 x 4 sin( x )5 arctg ( 4 x ) 3 1 3x 2),  ln( 125 x 2 ) ( 150 x75 x 23 ) arctg( 5 x ) 10 10 50 3), 4 ln( arcctg ( 5 x ) ), 4), 3 ln( ( 1x ) ( x4 ) ( x3 ) )

5), ln( 12 x )ln( x 26 x10 )10 arctg ( x3 ) 6), x 210 x24 x5 x 210 x24 ln( x5 x 210 x24 ) 7), ln( x5 x 210 x24 )( 3 x 2x1 ) x 210 x24 x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸3 ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 6 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ tg§ x ·1 © ©2¹ ¹ ¨¨ ¸¸ ©2¹ 2 · § x x 1 x 2 x 10), 6 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ·¸¸13 ¸¸16 arctg¨¨§ tg§¨¨ ¸¸· ¸¸·2 ln§¨¨ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹ © ©2¹ ¹

1), sin( 3 x )2 e (8 x )

4 arcsin( x )

( x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 39

2), ( 65 x9 x 2 ) e arccos( 8 x ) 4 3), 6 e , 4), ln( x3 )4 ln( x5 ) x5 x 1 5), 4 ln( x 28 x20 )12 arctg §¨¨ 2 ·¸¸ ln( 32 x ) ©2 ¹ 2 x 6), 12x 28 x x4 12x 28 x 4 arcsin§¨¨ 2 ·¸¸ ©2 ¹ x 1 7), ( 34 x 22 x ) 12x 24 x 3 arcsin§¨¨  ·¸¸ © 4 2¹ x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 2 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ ¸¸ ©2¹ 2 § · x x x x 10), 2 ln¨¨ tg¨¨§ ·¸¸ 4 tg¨¨§ ·¸¸5 ¸¸10 arctg ¨¨§ tg§¨¨ ¸¸·2 ¸¸·3 ln§¨¨ tg¨¨§ ¸¸·3 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 40

( 2 x ) 5x· 1), 5 e 5 arctg §¨¨ ¸¸4 cos( 2 x ) © 2 ¹ 1 2 x3 2), ( 6 x 336 x 29 x ) ln( 4 x ) 2 x 2x 9 9 3), 2 arctg( 2 x ) , 4), 2 ln( x3 )3 ln( x6 )3 ln( x2 ) x 3 5), 2 ln( x 24 x8 )4 arctg¨¨§ 1 ·¸¸ ln( 12 x ) ©2 ¹ 2 6), x 24 x32 x2 x 24 x32 36 ln( x2 x 24 x32 ) 7), ln( x2 x 24 x3 )( 5 x 22 x3 ) x 24 x3 x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 6 x x 9),  6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ·¸¸1 ©2¹ 2 § x x · x x 10), ln¨¨ 106 tg§¨¨ ¸¸·tg¨¨§ ¸¸· ¸¸10 arctg¨¨§ tg§¨¨ ¸¸·3 ¸¸·2 ln¨¨§ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 41

2

1), 3 cos( x )4 ln( x )6 x

( x8 ) 1x 1 1 2),  §¨ 4 x x 2 ·¸¸ arcsin( x ) 2 ©¨ 2 4 ¹ 1 3), 6 ln( cos( 9 x ) ), 4), ln( x3 )5 ln( x4 ) x4 2 x 5),  ln( 23 x )8 ln( x 28 x20 )36 arctg§¨¨ 2 ·¸¸ 3 2 © ¹ x 6), x 210 x x5 x 210 x 25 arcsin¨¨§ 1 ·¸¸ ©5 ¹ x 7), ( 25 x 2x ) 12x 28 x arcsin¨¨§ 2 ·¸¸ ©2 ¹ x x x 8), ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 6 9), 2 ln§ tg§ ·3 ·6 ln§ tg§ ·3 · ¨ ¨ ¸ ¸ ¨ ¨ ¸ ¸ ¨ ¨ ¸ ¸ ¨ ¨ ¸ ¸ © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ ¸¸ ©2¹ 2 · § x x 1 x x 10), 4 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·8 ¸¸12 arctg¨¨§ tg§¨¨ ¸¸·1 ¸¸·3 ln¨¨§ tg§¨¨ ·¸¸1 ¸¸· © ©2¹ ©2¹ ¹ ©2 © 2 ¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 42

2), ( 17 x9 x 2 ) e

(9 x )

1), 5 ln( x )6 x 4 sin( x )

arcsin( 4 x )

3), 2 e , 4), ln( x3 )2 ln( x2 )3 ln( 1x ) 3 5), 2 ln( 22 xx 2 )6 arctg( 1x ) ln( 1x ) 2 6), x 28 x9 x4 x 28 x9 25 ln( x4 x 28 x9 ) 7), 4 ln( x4 x 28 x15 )( 5 x 24 x1 ) x 28 x15 x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9),  6 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ·¸¸1 ©2¹ 2 § x x · 3 1 x x 10), 4 ln¨¨ 136 tg¨¨§ ¸¸·tg§¨¨ ¸¸· ¸¸16 arctg¨¨§  tg§¨¨ ¸¸· ¸¸·2 ln§¨¨ tg§¨¨ ·¸¸2 ¸¸· © ©2¹ ©2¹ ¹ ©2 2 © 2 ¹¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 43

5x· 1), 3 arcsin¨¨§ ¸¸4 ln( x )4 sin( 3 x ) © 3 ¹ 1 § x2 · 2), x ¨¨ ( 1212 xx 2 ) ln( 5 x )126 x ¸¸ 3 © 3 ¹ cos( 6 x ) 4 ln( x3 )3 ln( 1x ) 3), 4 e , 4),  1x x 2 5), 6 ln( x 24 x13 )4 arctg§¨¨  ·¸¸2 ln( x1 ) © 3 3¹ 6), 3x 24 x x2 3x 24 x arcsin( x2 ) x 5 7), ( 2 x4x 2 ) 21x 210 x 3 arcsin¨¨§  ·¸¸ © 2 2¹ x x x 8), ln§¨¨ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸2 ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

6 x x 9),  2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ·¸¸1 ©2¹ 2 § · x x x x 10), 2 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·5 ¸¸16 arctg¨¨§ tg§¨¨ ¸¸·2 ¸¸·2 ln¨¨§ tg§¨¨ ¸¸·3 ·¸¸ © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 44

4x· 1), 4 arcsin¨¨§ ¸¸5 cos( x )2 ln( x ) © 3 ¹ 2), sin( x )2 cos( x )2 sin( x ) x 3), 4 sin( 4 x ) , 4), 2 ln( 3x )2 ln( x4 )3 ln( x2 ) x 1 5), 12 ln( 102 xx 2 )16 arctg §¨¨  ·¸¸ln( 12 x ) © 3 3¹ 6), x 210 x11 x5 x 210 x11 36 ln( x5 x 210 x11 ) 7), 4 ln( x4 x 28 x15 )( 4 x 2x4 ) x 28 x15 x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·ln¨¨§ tg¨¨§ ¸¸·1 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 6 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹ 2 § · x x x x 10), ln¨¨ tg¨¨§ ¸¸· 6 tg§¨¨ ¸¸·10 ¸¸8 arctg¨¨§ tg¨¨§ ¸¸·3 ¸¸·3 ln¨¨§ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

(9 x )

1), sin( 4 x )3 ln( x )8 x

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 45

2), ( 93 x5 x 2 ) e 1 3), 8 arccos ( 9 x ) , 4), 5 ln( x3 ) ln( x4 ) x4 2 5), 4 ln( x 28 x17 )28 arctg ( x4 ) ln( x1 ) 3 x 6), x 24 x x2 x 24 x 4 arcsin§¨¨ 1 ·¸¸ ©2 ¹ x 5 7), ( 4 x23 x 2 ) 21x 210 x 5 arcsin¨¨§  ·¸¸ © 2 2¹ x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸3 ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ¸¸·2 ©2¹ 2 § · x x 1 x 1 x 10), 2 ln¨¨ tg¨¨§ ·¸¸ 2 tg¨¨§ ·¸¸5 ¸¸4 arctg¨¨§ tg¨¨§ ·¸¸ ·¸¸2 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸· © ©2¹ ©2¹ ¹ ©2 © 2 ¹ 2¹ © ©2¹ ¹ (4 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 46

1), 3 sin( x )2 x 3 e 1 x3 7 x2 ( 12 x 3126 x 2252 x ) ln( 5 x )  2), 7 x 9 4 36 3), 6 cos( 5 x ) , 4), 3 ln( 3x )ln( x5 )2 ln( x1 ) 5), ln( ( 12 x ) ( x 24 x5 ) ) 6), x 26 x10 x3 x 26 x10 ln( x3 x 26 x10 )

7), 4 ln( x3 86 xx 2 )( 35 x4 x 2 ) 86 xx 2

x x x 8), 3 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 4 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 4 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹ 2 § · x x x 10), 6 ln¨¨ tg¨¨§ ·¸¸ 2 tg§¨¨ ¸¸·10 ¸¸ln¨¨§ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹

( x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 47

1), 5 arcsin( x )6 x 5 e 1 1 2 sin( 5 x ) cos( 5 x ) x cos( 5 x ) 2), 25 5 5 3 3), 6 arctg ( 8 x ) , 4),  4 ln( x3 )2 ln( x4 ) x4 1 5), 2 ln( 22 xx 2 ) ln( 13 x ) 3 x 5 6), 21x 210 x x5 21x 210 x 4 arcsin§¨¨  ·¸¸ © 2 2¹ 7), ( 14 x3 x 2 ) 86 xx 2 2 arcsin( 3x ) x x x 8), 3 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·3 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 6 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ tg§ x ·1 © ©2¹ ¹ ¨ ¸ ¨ ¸ ©2¹ 2 · § x x x 1 1 x 10), ln§¨¨ tg§¨¨ ·¸¸3 ¸¸·6 ln¨¨ tg¨¨§ ¸¸· 2 tg§¨¨ ¸¸·10 ¸¸8 arctg¨¨§   tg§¨¨ ¸¸· ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © 3 3 © 2 ¹¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 48

7x· 1), 4 cos( 2 x )3 arcsin( 6 x )arctg ¨¨§ ¸¸ © 2 ¹ ( 4 x ) 2), ( 56 x9 x 2 ) e 3), 8 ln( arcctg ( 8 x ) ), 4), 2 ln( 3x )ln( x5 )3 ln( x1 ) 3 x 2 5), ln( 12 x )3 ln( x 24 x13 )12 arctg§¨  ·¸ ¨ ¸ 2 © 3 3¹ §x x 28 x32 ·¸ 6), x 28 x32 x4 x 28 x32 16 ln¨¨ 1 ¸ 4 ©4 ¹ 7), 3 ln( 3x 106 xx 2 )( 42 x2 x 2 ) 106 xx 2 x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 6 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· 4 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹ 2 · § x x x x 10), 2 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·5 ¸¸4 arctg¨¨§ tg§¨¨ ¸¸·2 ¸¸·2 ln¨¨§ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

1), 4 ln( x )3 cos( 5 x )6 x

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 49

2

1 2 x3 3 x2 2), ( 12 x 318 x 236 x ) ln( 4 x )  6 x 6 3 2 2 3), 6 arcctg ( 6 x ) , 4), 5 ln( 1x )4 ln( x1 ) 1x x 1 5), 2 ln( x3 )4 ln( x 22 x5 )6 arctg¨¨§  ·¸¸ © 2 2¹ 1 x 6), 8x 22 x x 8x 22 x 9 arcsin§¨¨   ·¸¸ © 3 3¹ x 5 7), ( 43 x 2x ) 9x 210 x arcsin¨¨§  ·¸¸ © 4 4¹ x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ 2 ¸¸ © ¹ § · x x x 1 x 2 10), 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·6 ln¨¨ tg§¨¨ ·¸¸ 4 tg¨¨§ ·¸¸13 ¸¸6 arctg¨¨§ tg¨¨§ ·¸¸ ·¸¸ © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹

( 4 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 50

1), arcsin( 3 x )6 x 2 e 1 1 3x 3 2), ln( 125 x 2 ) ( 100 x75 x 2 ) arcctg ( 5 x )  arctg ( 5 x ) 5 50 10 50 3), 8 cos( 3 x ) , 4), 2 ln( 3x )2 ln( x4 )2 ln( x2 ) 5), 2 ln( 22 xx 2 )8 arctg( 1x )ln( 1x ) 6), x 28 x48 x4 x 28 x48 64 ln( x4 x 28 x48 )

7), 2 ln( x3 x 26 x10 )( x 25 x4 ) x 26 x10 x x x 8), ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 4 x x 9), 2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ¸¸·1 ©2¹ 2 · § x x x 1 x 10), 2 ln§¨¨ tg§¨¨ ¸¸·1 ¸¸·6 ln¨¨ tg¨¨§ ¸¸· 6 tg§¨¨ ·¸¸18 ¸¸14 arctg¨¨§ tg§¨¨ ·¸¸1 ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹

( 2 x )

1), 2 arctg ( 7 x )5 sin( x )10 x

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 51

2), ( 76 x2 x 2 ) e arcctg( 3 x ) 3 3), 8 e , 4),  ln( x3 )2 ln( x4 ) x4 x 1 5), 2 ln( x 22 x5 )10 arctg§¨¨  ·¸¸2 ln( 1x ) © 2 2¹ x 6), x 24 x x2 x 24 x 4 arcsin§¨¨ 1 ·¸¸ ©2 ¹ 7), ( 2x 25 x ) 24x 210 x arcsin( x5 ) x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 6 x 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·2 ¨¨ ¸¸ ©2¹

2

§ · x x x x 10), ln¨¨ tg¨¨§ ¸¸· 6 tg§¨¨ ¸¸·10 ¸¸8 arctg¨¨§ tg¨¨§ ¸¸·3 ¸¸·3 ln¨¨§ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 52

( 2 x ) 5x · 1), 5 arctg §¨¨ ¸¸4 ln( x )5 e © 3 ¹ 4 § x2 3 x · 2), x ¨¨ ( x 23 x6 ) ln( 3 x )  6 ¸¸ 3 © 2 3 ¹ arctg( 5 x ) 3), 2 e , 4), 2 ln( x6 )ln( 1x )2 ln( x1 ) x 5), ln( 32 x )12 ln( x 26 x18 )32 arctg¨¨§ 1 ·¸¸ ©3 ¹ §x 1 x 22 x17 ¸· 6),  x 22 x17  x 22 x17 x16 ln¨¨   ¸ 4 ©4 4 ¹ 7), ln( x4 x 28 x15 )( 3 x33 x 2 ) x 28 x15 x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸2 ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 4 x 9), 2 ln§ tg§ ·4 · 4 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· ¨ ¨ ¸ ¸ ¨ ¨ ¸ ¸ © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹ 2 · § x x 1 x x 10), 8 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·8 ¸¸24 arctg¨¨§ tg§¨¨ ¸¸·1 ¸¸·2 ln¨¨§ tg§¨¨ ·¸¸1 ¸¸· © ©2¹ ©2¹ ¹ ©2 © 2 ¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 53

5x· 1), 4 arcsin( x )5 cos( 3 x )3 arctg§¨¨ ¸¸ © 4 ¹ 1 1 x 1 2),  ln( 19 x 2 ) ( 9 x 218 x ) arcctg ( 3 x )  arctg ( 3 x ) 2 6 2 6

4 3), 2 ln( arctg ( 4 x ) ), 4),  3 ln( x2 )ln( x5 ) x5 x 5), ln( x2 )3 ln( x 26 x18 )2 arctg§¨¨ 1 ·¸¸ ©3 ¹ x 6), x 28 x x4 x 28 x 16 arcsin§¨¨ 1 ·¸¸ ©4 ¹ x 7), ( 3 x2x 2 ) 12x 28 x arcsin§¨¨ 2 ·¸¸ ©2 ¹ x x x 8), 3 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 6 x 9), 4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·2 ¨¨ ¸¸ ©2¹ 2 · § x x 1 x 2 x 10), 12 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·13 ¸¸12 arctg§¨¨ tg§¨¨ ¸¸· ¸¸·ln¨¨§ tg§¨¨ ·¸¸2 ¸¸· © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹ © ©2¹ ¹

( 8 x )

1), 8 x 3 cos( 4 x )4 sin( 4 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 54

( 78 x4 x 2 ) 2), e 3), 4 arcctg ( 4 x ) , 4), 3 ln( x3 )3 ln( x2 )3 ln( x2 ) x 5), 4 ln( x 24 x8 )10 arctg§¨¨ 1 ·¸¸2 ln( x3 ) ©2 ¹

6), x 210 x16 x5 x 210 x16 9 ln( x5 x 210 x16 ) 7), 3 ln( x1 22 xx 2 )( 43 xx 2 ) 22 xx 2 x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸2 ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ln¨¨§ tg¨¨§ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ ¸¸ ©2¹ 2 § x x · 1 x x 10), 12 ln¨¨ 186 tg¨¨§ ¸¸·tg§¨¨ ¸¸· ¸¸32 arctg¨¨§ tg§¨¨ ¸¸·1 ¸¸·ln¨¨§ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 55

5x· 1), 5 arctg §¨ ¸2 arcsin( 3 x )6 x ¨ ¸ © 4 ¹ 1 7 x2 2), ( 12 x 314 x 24 x ) ln( 3 x )x 3 x 4 4 3 3), 2 arccos ( 4 x ) , 4), 4 ln( 1x )3 ln( x1 ) 1x 3 5),  ln( 12 x )4 ln( 106 xx 2 )20 arctg ( 3x ) 2 x 1 6), 15x 22 x  15x 22 x x16 arcsin§¨¨  ·¸¸ © 4 4¹ x 4 7), ( 32 x 2x ) 7x 28 x 2 arcsin§¨¨  ·¸¸ © 3 3¹ x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸2 ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9),  4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ¸¸·1 ©2¹ 2 · § x x 1 x x 10), 8 ln¨¨ tg¨¨§ ¸¸· 4 tg¨¨§ ·¸¸8 ¸¸8 arctg¨¨§ tg§¨¨ ¸¸·1 ¸¸·3 ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ©2¹ ¹ ©2 © 2 ¹ ¹ © ©2¹ ¹

1), 4 cos( 3 x )2 ln( x )3 sin( 3 x ) 1 1 x ln( 19 x 2 ) ( 9 x 254 x1 ) arctg ( 3 x ) 2 18 6

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 56

2), sin( 8 x )

3), 2 e , 4), ln( x3 )3 ln( x5 )3 ln( 1x ) x 2 5), ln( 13 x )3 ln( x 24 x13 )2 arctg§¨¨  ·¸¸ © 3 3¹ 6), x 26 x5 x3 x 26 x5 4 ln( x3 x 26 x5 )

7), 2 ln( 3x 106 xx 2 )( 25 x5 x 2 ) 106 xx 2 x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 6 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 6 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·2 ¨¨ ¸¸ ©2¹ 2 § x x x · x 10), ln§¨¨ tg§¨¨ ¸¸·2 ¸¸·4 ln¨¨ 106 tg§¨¨ ¸¸·tg¨¨§ ¸¸· ¸¸32 arctg¨¨§ tg§¨¨ ¸¸·3 ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 57

( 5 x ) 7x· 1), 4 cos( 2 x )4 arctg¨¨§ ¸¸4 e © 2 ¹ ( 2 x ) 2), ( 94 x3 x 2 ) e arcctg( 5 x ) 1 3), 8 e , 4), 3 ln( x5 ) 3 ln( x1 ) x5 x 5), ln( 32 x )3 ln( x 26 x18 )10 arctg¨¨§ 1 ·¸¸ ©3 ¹ x 1 6), 3 276 xx 2  276 xx 2 x36 arcsin¨¨§  ·¸¸ © 6 2¹ x 7), ( 1x 22 x ) x 28 x 5 arcsin§¨¨ 1 ·¸¸ ©4 ¹ x x x 8), 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸3 ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 6 x x 9),  6 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ¸¸·1 ©2¹ 2 § x x · 1 x x 10), 6 ln¨¨ 186 tg¨¨§ ¸¸·tg§¨¨ ¸¸· ¸¸14 arctg¨¨§ tg§¨¨ ¸¸·1 ¸¸·3 ln¨¨§ tg§¨¨ ·¸¸2 ¸¸· © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹ © ©2¹ ¹

cos( 6 x )

1), 5 ln( x )5 e x 2 arcsin( 2 x ) 1 x3 ( 3 x 36 x 29 x ) ln( 8 x ) x 23 x 3 3

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 58

2),

3), 6 e , 4), 2 ln( x3 )ln( x2 )ln( 1x ) 5), 3 ln( 3x )2 ln( 22 xx 2 ) 6), x 28 x20 x4 x 28 x20 36 ln( x4 x 28 x20 )

7), 5 ln( x1 x 22 x )( 2 x 25 x3 ) x 22 x x x x 8), ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ ¸¸ ©2¹ 2 · § x x 1 1 x x 10), 8 ln¨¨ tg¨¨§ ¸¸· 2 tg¨¨§ ·¸¸5 ¸¸12 arctg¨¨§   tg§¨¨ ¸¸· ¸¸·ln¨¨§ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ © 2 2 © 2 ¹¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 59

7x· 1), 4 cos( 4 x )arcsin( 5 x )3 arctg¨¨§ ¸¸ © 4 ¹ 1 1 3 2),  cos( 5 x ) sin( 5 x ) x sin( 5 x ) 25 5 5 2 3), 6 arccos ( 2 x ) , 4), 2 ln( x2 ) 5 ln( 1x ) 1x x 1 5), 2 ln( 3x )8 ln( x 22 x5 )10 arctg§¨¨  ·¸¸ © 2 2¹ 6), 15x 28 x x4 15x 28 x arcsin( x4 ) x 1 7), ( 3 x 24 x3 ) 15x 22 x arcsin¨¨§  ·¸¸ © 4 4¹ x x x 8), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

6 x x 9), 4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· x 2 2 © © ¹ ¹ © © ¹ ¹ tg¨¨§ ·¸¸2 ©2¹ 2 § · x x x 1 x 2 10), ln§¨¨ tg§¨¨ ¸¸·3 ¸¸·3 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·13 ¸¸6 arctg¨¨§ tg§¨¨ ¸¸· ·¸¸ © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 60 (6 x )

1), 4 x 5 sin( 3 x )3 cos( 5 x )

( 14 xx 2 ) 2), e 3), 4 ln( arcsin( 2 x ) ), 4), ln( x2 )3 ln( x6 )ln( x2 ) 5), 2 ln( x 28 x17 )20 arctg ( x4 )ln( 1x )

6), x 210 x x5 x 210 x 25 ln( x5 x 210 x ) 7), 5 ln( x2 x 24 x5 )( 2 x 2x5 ) x 24 x5 x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸2 ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 4 x x 9), 4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ·¸¸1 ©2¹ 2 § · x x 1 x 1 x 10), 6 ln¨¨ tg¨¨§ ¸¸· 2 tg§¨¨ ¸¸·10 ¸¸8 arctg¨¨§ tg§¨¨ ¸¸· ¸¸·ln¨¨§ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 61

1), 8 x 4 ln( x )5 arcsin ( 5 x ) 1 5 x3 7 x2 ( 60 x 3126 x 2252 x ) ln( 3 x ) 2),  7 x 9 4 36 5 3), 8 ln( arccos ( 7 x ) ), 4), 4 ln( x3 ) 4 ln( 1x ) 1x x 1 5), 6 ln( 102 xx 2 )12 arctg §¨¨  ·¸¸ln( 12 x ) © 3 3¹ x 1 6), 82 xx 2  82 xx 2 x9 arcsin¨¨§  ·¸¸ © 3 3¹ 7), ( 2 x 25 x2 ) x 22 x 2 arcsin( 1x ) 2 3 § x x x · 8), 2 ln¨¨ 2 tg¨¨§ ·¸¸ 6tg§¨¨ ·¸¸ 5 tg¨¨§ ·¸¸ ¸¸ © ©2¹ ©2¹ © 2 ¹¹ x x 4 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ ¸¸ ©2¹ 2 § x x x · x 10), 2 ln§¨¨ tg§¨¨ ·¸¸2 ¸¸·2 ln¨¨ 106 tg¨¨§ ¸¸·tg¨¨§ ¸¸· ¸¸20 arctg¨¨§ tg§¨¨ ¸¸·3 ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © ©2¹ ¹

1), 2 e cos( 5 x )2 x 1 1 3x 3 ln( 116 x 2 ) ( 32 x48 x 2 ) arcctg ( 4 x )  arctg ( 4 x ) 8 32 32 8

( 2 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 62

2),

cos( 4 x )

3), 8 e , 4), 3 ln( 3x )3 ln( x3 )ln( x5 ) 5), 3 ln( x3 )8 ln( x 22 x5 ) 6), 3 6 xx 2  6 xx 2 x9 ln( x3 6 xx 2 ) 7), 4 ln( x5 x 210 x26 )( 2 x 24 x5 ) x 210 x26

x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸2 ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 4 x x 9), 6 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ¸¸·1 ©2¹ 2 § x x x · x 10), 3 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·4 ln¨¨ 22 tg¨¨§ ·¸¸tg§¨¨ ·¸¸ ¸¸12 arctg§¨¨ tg§¨¨ ·¸¸1 ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 63

(5 x ) 7x· 1), 3 e 2 arctg §¨¨ ¸¸3 sin( 5 x ) © 2 ¹ (3 x ) 2), ( 89 x9 x 2 ) e 4 3), 4 ln( sin( 5 x ) ), 4),  ln( x2 )3 ln( x5 ) x5 x 2 3 5), 6 ln( x 24 x13 )10 arctg ¨¨§  ·¸¸ ln( x1 ) © 3 3¹ 2 x 2 6), 20x 28 x x4 20x 28 x 36 arcsin§¨¨  ·¸¸ © 6 3¹ x 4 7), ( 2 x22 x 2 ) 7x 28 x 2 arcsin§¨¨  ·¸¸ © 3 3¹ x x x 8), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·3 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9),  2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ¸¸·2 ©2¹ 2 § · x x x 1 1 x 10), 2 ln§¨¨ tg§¨¨ ¸¸·1 ¸¸·12 ln¨¨ tg¨¨§ ¸¸· 2 tg§¨¨ ¸¸·10 ¸¸10 arctg¨¨§   tg§¨¨ ¸¸· ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © 3 3 © 2 ¹¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 64

1), arcsin( 7 x )4 cos( 4 x )2 ln( x ) 1 8 x3 9 x2 ( 96 x 3162 x 2108 x ) ln( 8 x ) 2),  3 x 9 4 36 3), 4 arccos ( 8 x ) , 4), ln( x4 )2 ln( x6 )2 ln( x2 ) 2 x 5),  ln( x1 )12 ln( x 26 x18 )16 arctg¨¨§ 1 ·¸¸ 3 ©3 ¹ §x 5 x 210 x41 ¸· 6), x 210 x41 x5 x 210 x41 16 ln¨¨   ¸ 4 ©4 4 ¹ 7), 2 ln( x3 86 xx 2 )( 12 x3 x 2 ) 86 xx 2 x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸2 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· © ©2¹ ¹ © ©2¹ ¹ §x· tg ¨¨ ¸¸3 ©2¹ 2 3 § x x x · 10), 2 ln¨¨ 6 tg¨¨§ ·¸¸ 10tg¨¨§ ·¸¸ 13 tg¨¨§ ·¸¸ ¸¸ © ©2¹ ©2¹ © 2 ¹¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 65

5x· §7x· 1), 2 ln( x )2 arctg§¨¨ ¸¸2 arcsin¨¨ 4 ¸¸ © 2 ¹ © ¹ 2), 2 cos( x )2 sin( x ) x2 sin( x )

4 3), 4 ln( arccos ( 9 x ) ), 4), 2 ln( 3x ) 5 ln( x1 ) 3x x 1 1 5), 8 ln( x 22 x5 )10 arctg§¨¨  ·¸¸ ln( 1x ) © 2 2¹ 3 x 4 6), 7x 28 x x4 7x 28 x 9 arcsin§¨¨  ·¸¸ © 3 3¹ x 7), ( 2 x33 x 2 ) 12x 28 x 2 arcsin§¨¨ 2 ·¸¸ ©2 ¹ x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 2 9), 2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ §x· tg ¨¨ ¸¸2 ©2¹ 2 · § §x· · · § §x· ¸ ¸32 arctg¨¨ tg¨¨ 2 ¸¸3 ¸¸2 ln¨¨ tg¨¨ 2 ¸¸1 ¸¸ ¹ © © ¹ ¹ © © ¹ ¹

§ x x 10), 4 ln¨¨ 106 tg¨¨§ ¸¸·tg§¨¨ ¸¸· © ©2¹ ©2¹

( 3 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 66

1), 5 ln( x )10 x e 2), ( 82 x6 x 2 ) e x 3), 6 ln( arcsin( 4 x ) ), 4), 2 ln( 3x )ln( x4 ) x 5), 8 ln( x 24 x8 )12 arctg §¨¨ 1 ·¸¸ln( 13 x ) ©2 ¹ 6),  x 22 x  x 22 x xln( x1 x 22 x ) 7), ln( 1x 22 xx 2 )( 45 x5 x 2 ) 22 xx 2 x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 4 x 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· 6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨ ¸ ¨ ¸ ©2¹ 2 § · x x x 1 1 x 10), 2 ln§¨¨ tg§¨¨ ¸¸·3 ¸¸·12 ln¨¨ tg¨¨§ ¸¸· 2 tg§¨¨ ¸¸·10 ¸¸4 arctg¨¨§   tg§¨¨ ¸¸· ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © 3 3 © 2 ¹¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 67

x tg¨¨§ ¸¸·2 ©2¹

1), 3 arctg( 2 x )6 x 5 ln( x ) 1 5 x3 7 x2 ( 60 x 3126 x 2108 x ) ln( 4 x ) 2),  3 x 36 9 4 4 3), 2 ln( arctg ( 8 x ) ), 4), 3 ln( 3x ) 5 ln( x2 ) 3x 3 x 5), ln( 32 x )3 ln( x 26 x18 )4 arctg§¨¨ 1 ·¸¸ 2 ©3 ¹ 3 x 6), 3 56 xx 2  56 xx 2 x4 arcsin¨¨§  ·¸¸ ©2 2 ¹ x 4 7), ( 13 x 2x ) 7x 28 x 2 arcsin§¨¨  ·¸¸ © 3 3¹ x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 6 x x 6 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹

9), 

2

§ x x · 1 x x 10), 12 ln¨¨ 186 tg§¨¨ ¸¸·tg¨¨§ ¸¸· ¸¸20 arctg¨¨§ tg§¨¨ ¸¸·1 ¸¸·ln¨¨§ tg§¨¨ ·¸¸2 ¸¸· © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 68

1), 3 ln( x )8 x 5 sin( x ) 2), cos( x )sin( x ) xsin( x ) 3), 4 sin( 4 x ) , 4), 3 ln( 3x )2 ln( x3 )ln( x1 )

x 2 5), 4 ln( x 28 x20 )12 arctg §¨¨ 2 ·¸¸ ln( 23 x ) ©2 ¹ 3 §x 1 x 22 x65 ¸· 6),  x 22 x65  x 22 x65 x64 ln¨¨   ¸ 8 ©8 8 ¹ 7), 4 ln( x1 x 22 x )( 3 x43 x 2 ) x 22 x x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 2 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨ ¸ ¨ ¸ ©2¹ 2 · · § §x· ¸ ¸4 arctg¨¨ tg¨¨ 2 ¸¸1 ¸¸ ¹ © © ¹ ¹

§ x x x 10), 3 ln§¨¨ tg¨¨§ ·¸¸3 ·¸¸2 ln¨¨ 22 tg¨¨§ ·¸¸tg§¨¨ ·¸¸ © ©2¹ ¹ © ©2¹ ©2¹

5 5 ln( x1 ) 1x

(8 x )

3 ln( x )arcsin( 2 x )

(4 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 69

2), ( 86 x4 x 2 ) e

1), 2 e

3), 6 ln( arcsin( 5 x ) ), 4), ln( 1x )

x 1 5), 8 ln( x 28 x20 )36 arctg ¨¨§ 2 ·¸¸ ln( x1 ) ©2 ¹ 2 x 5 6), 11x 210 x x5 11x 210 x 36 arcsin¨¨§  ·¸¸ © 6 6¹ x 7), ( 22 x 23 x ) 12x 28 x arcsin¨¨§ 2 ·¸¸ ©2 ¹ x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 4 ln¨§¨ tg¨§¨ ¸·¸2 ¸·¸ 6 ln¨§¨ tg¨§¨ ¸·¸2 ¸·¸ © ©2¹ ¹ © ©2¹ ¹ tg§ x ·2 ¨¨ 2 ¸¸ © ¹ 2 · § x x x 1 x 2 10), 3 ln§¨¨ tg¨¨§ ¸¸·3 ¸¸·3 ln¨¨ tg¨¨§ ·¸¸ 4 tg§¨¨ ¸¸·13 ¸¸8 arctg¨¨§ tg§¨¨ ¸¸· ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 70

5x· 1), 4 cos( 2 x )sin( 3 x )5 arcsin¨§ ¸ ¨ ¸ © 4 ¹ 1 7 x3 9 x2 ( 84 x 3162 x 2216 x ) ln( 8 x ) 2),  6 x 9 4 36 3), 2 ln( cos( 3 x ) ), 4), ln( x5 )3 ln( x1 )3 ln( x2 ) 5), ln( 12 x )4 ln( x 28 x17 )30 arctg ( x4 ) 6), x 22 x48 x x 22 x48 49 ln( x1 x 22 x48 ) 7), 5 ln( x5 x 210 x26 )( 3 x5x 2 ) x 210 x26

x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9), 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ¸¸·1 ©2¹ 2 § · x x x 10), 3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·6 ln¨¨ tg§¨¨ ·¸¸ 2 tg¨¨§ ·¸¸10 ¸¸ © ©2¹ ¹ © ©2¹ ©2¹ ¹

( x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 71

, 4),

1), 5 ln( x )4 e 2 sin( 4 x ) ( 3 x12 ) 19 x 2 1 1 2),  ( 36 x18 x 2 ) arccos ( 3 x ) arcsin( 3 x ) 12 12 12 sin( 2 x ) 5 2 ln( x2 )4 ln( x5 ) x5

3), 2 e

3 x 1 5), 4 ln( 136 xx 2 )20 arctg§¨¨  ·¸¸ ln( 32 x ) ©2 2 ¹ 2 x 1 6), 3 276 xx 2  276 xx 2 x36 arcsin¨¨§  ·¸¸ © 6 2¹ 7), ( 14 x 23 x ) 24x 210 x arcsin( x5 ) x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· © ©2¹ ¹ © ©2¹ ¹ §x· tg ¨¨ ¸¸3 ©2¹ 2 § · x x x 1 x 2 10), 2 ln§¨¨ tg¨¨§ ¸¸·2 ¸¸·12 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·13 ¸¸14 arctg¨¨§ tg§¨¨ ·¸¸ ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 72

7x· 1), arctg( 2 x )6 x 3 arcsin¨¨§ ¸¸ © 4 ¹ (6 x ) 2), ( 59 x7 x 2 ) e 3), 8 sin( 4 x ) , 4), ln( 3x )ln( x4 )2 ln( x2 ) 2 5), ln( 23 x )ln( 106 xx 2 )10 arctg ( 3x ) 3 6), x 210 x16 x5 x 210 x16 9 ln( x5 x 210 x16 ) 7), 5 ln( 1x 22 xx 2 )( 4xx 2 ) 22 xx 2 x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 6 9), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ ¸¸ ©2¹ 2 · § x x x 10), 6 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·13 ¸¸ln¨¨§ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹

1), 4 sin( 3 x )6 x 2 e 1 7 x3 7 x2 ( 84 x 3126 x 272 x ) ln( 2 x )  2 x 36 9 4

( x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 73

2),

cos( 9 x ) 5 3), 6 e , 4), 2 ln( x2 )5 ln( x5 ) x5 1 x 5), 3 ln( x3 )12 ln( x 22 x10 )12 arctg §¨¨   ·¸¸ © 3 3¹ x 5 6), 24x 210 x x5 24x 210 x 49 arcsin¨¨§  ·¸¸ © 7 7¹ x 7), ( 4 x35 x 2 ) 6 xx 2 arcsin¨¨§ 1 ·¸¸ ©3 ¹ x x x 8), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸2 ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 4 x 9), 4 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹ 2 § · x x x 1 x 10), 2 ln§¨¨ tg¨¨§ ¸¸·2 ¸¸·3 ln¨¨ tg¨¨§ ·¸¸ 6 tg§¨¨ ¸¸·18 ¸¸2 arctg¨¨§ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 74

5x· 1), 4 x 4 arctg§¨¨ ¸¸3 sin( x ) © 3 ¹ 2), cos( x )sin( x ) x2 sin( x )

arcctg( 4 x )

3), 2 e , 4), 2 ln( 3x )3 ln( x4 )3 ln( x3 ) x 5), ln( x1 )3 ln( x 26 x18 )4 arctg§¨¨ 1 ·¸¸ ©3 ¹ 6), x 28 x9 x4 x 28 x9 25 ln( x4 x 28 x9 ) 7), 2 ln( x5 x 210 x24 )( 4 x54 x 2 ) x 210 x24 x x x 8), 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9), 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ¸¸·1 ©2¹ 2 · § x x 1 x x 10), 12 ln¨¨ tg¨¨§ ¸¸· 6 tg§¨¨ ¸¸·18 ¸¸26 arctg¨¨§ tg§¨¨ ¸¸·1 ¸¸·2 ln¨¨§ tg§¨¨ ¸¸·2 ·¸¸ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹ © ©2¹ ¹

( 7 x )

1), 3 sin( 2 x )4 x 4 arcsin ( x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 75

2), e ( 42 x3 x 2 ) cos( 3 x ) 1 3), 2 e , 4), 4 ln( x3 ) 2 ln( 1x ) 1x 5), ln( 22 xx 2 )10 arctg( x1 )ln( 1x ) 6), 24x 210 x x5 24x 210 x arcsin( x5 ) 7), ( 2 x33 x 2 ) x 22 x 2 arcsin( 1x ) x x x 8), ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 4 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ 2 ¸¸ © ¹ 2 § · x x x 1 1 x 10), ln§¨¨ tg§¨¨ ·¸¸1 ¸¸·6 ln¨¨ tg¨¨§ ¸¸· 2 tg§¨¨ ¸¸·10 ¸¸2 arctg¨¨§   tg§¨¨ ¸¸· ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © 3 3 © 2 ¹¹

______________________________________________________

ȼɚɪɢɚɧɬ ʋ 76

2

(5 x ) 5x· 5x· 1), 4 arcsin¨¨§ 3 arctg ¨¨§ ¸¸2 e ¸¸ © 3 ¹ © 4 ¹ 8§ 27 27 x x 2 ·  ¸¸ x 2),  ¨¨ §¨¨ 3 xx 2 ·¸¸ ln( 9 x )3 3 ¹ 3 16 32 © © ¹ 3), 8 arccos ( 5 x ) , 4), 3 ln( x3 )2 ln( x2 )3 ln( 1x ) x 5), 2 ln( x 24 x8 )12 arctg§¨¨ 1 ·¸¸3 ln( 1x ) ©2 ¹ §x 5 x 210 x61 ¸· 6), x 210 x61 x5 x 210 x61 36 ln¨¨   ¸ 6 ©6 6 ¹ 7), 2 ln( x3 86 xx 2 )( 55 x4 x 2 ) 86 xx 2 x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸2 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 6 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨ ¸ ¨ ¸ ©2¹ · § §x· · · § §x· ¸ ¸4 arctg¨¨ tg¨¨ 2 ¸¸1 ¸¸ln¨¨ tg¨¨ 2 ¸¸2 ¸¸ ¹ © © ¹ ¹ © © ¹ ¹

§ x x 10), 2 ln¨¨ 22 tg§¨¨ ¸¸·tg§¨¨ ¸¸· © ©2¹ ©2¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 77

1), 3 arctg ( 3 x )10 x 2 sin( x ) 2), sin( x )cos( x ) x2 cos( x ) arcctg( 2 x ) 5 3), 8 e , 4), 3 ln( x3 ) 2 ln( x2 ) x2 1 5), 4 ln( 22 xx 2 )16 arctg ( 1x ) ln( 32 x ) 2 x 1 6), 352 xx 2  352 xx 2 x36 arcsin¨¨§  ·¸¸ © 6 6¹ x 3 7), ( 42 x2 x 2 ) 76 xx 2 4 arcsin¨¨§  ·¸¸ © 4 4¹ x x x 8), ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 4 x x 9),  6 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ·¸¸1 ©2¹ 2 § x x · 1 x x 10), 6 ln¨¨ 186 tg§¨¨ ·¸¸tg§¨¨ ·¸¸ ¸¸20 arctg §¨¨ tg¨¨§ ·¸¸1 ·¸¸ln¨¨§ tg¨¨§ ·¸¸3 ¸¸· © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹ © ©2¹ ¹ ( x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 78

1), 5 e 3 sin( 3 x )4 ln( x ) 2), ( 18 x2 x 2 ) e x sin( 2 x )

3), 8 e , 4), 2 ln( 3x )ln( x4 )2 ln( x1 ) 5), 3 ln( x3 )ln( x 28 x17 )16 arctg ( x4 ) 6), x 28 x9 x4 x 28 x9 25 ln( x4 x 28 x9 ) 7), 4 ln( x1 22 xx 2 )( 4x2 x 2 ) 22 xx 2 x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

x x 4 9), 2 ln¨§¨ tg¨§¨ ¸·¸3 ¸·¸4 ln¨§¨ tg¨§¨ ¸·¸4 ¸·¸ © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 § · x x x 10), 3 ln§¨¨ tg¨¨§ ¸¸·3 ¸¸·12 ln¨¨ tg¨¨§ ¸¸· 2 tg§¨¨ ¸¸·10 ¸¸ © ©2¹ ¹ © ©2¹ ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 79

7x· 1), sin( 3 x )3 arcsin¨§ ¸6 x ¨ ¸ © 3 ¹ 1 2 x3 9 x2 ( 24 x 354 x 212 x ) ln( 7 x ) 2),  x 12 3 4 arcsin( 6 x ) 4 4 ln( x1 ) 3), 4 e , 4), 2 ln( 3x ) 3x 1 1 x 5), ln( 13 x )12 ln( x 22 x10 )12 arctg ¨¨§   ·¸¸ 3 © 3 3¹ 3 x 6), 3 56 xx 2  56 xx 2 x4 arcsin¨¨§  ·¸¸ ©2 2 ¹ x 5 7), ( 35 x 23 x ) 21x 210 x 5 arcsin¨¨§  ·¸¸ © 2 2¹ x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸3 ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 2 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· © ©2¹ ¹ © ©2¹ ¹ §x· tg ¨¨ ¸¸3 ©2¹ 2 § · x x x 1 1 x 10), 3 ln§¨¨ tg§¨¨ ¸¸·3 ¸¸·6 ln¨¨ tg¨¨§ ·¸¸ 2 tg§¨¨ ·¸¸10 ¸¸2 arctg¨¨§   tg§¨¨ ¸¸· ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © 3 3 © 2 ¹¹

1), 5 e

5 sin( 2 x )arctg( 6 x )

( 3 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 80

( 5 x20 ) 125 x 2 1 1 ( 50 x 2100 x ) arccos ( 5 x ) arcsin( 5 x ) 2),  100 100 100 3), 4 ln( arctg( 6 x ) ), 4), 3 ln( 3x )3 ln( x3 )2 ln( x5 ) x 5), ln( x3 )3 ln( x 26 x18 )2 arctg§¨¨ 1 ·¸¸ ©3 ¹ §x 2 x 24 x29 ¸· 6), x 24 x29 x2 x 24 x29 25 ln¨¨   ¸ 5 ©5 5 ¹ 7), 5 ln( x1 22 xx 2 )( 1x4 x 2 ) 22 xx 2 x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 4 x x 9),  6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ¸¸·1 ©2¹ 2 § · x x x 10), 2 ln¨¨ tg¨¨§ ·¸¸ 4 tg¨¨§ ·¸¸5 ¸¸ln¨¨§ tg¨¨§ ·¸¸1 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 81

2), ( 63 x8 x 2 ) e

( x )

1), 2 sin( 4 x )3 cos( 5 x )2 ln( x )

arcsin( 6 x ) 4 3), 6 e , 4),  ln( 3x )2 ln( x2 ) 3x 1 5), 4 ln( 22 xx 2 )16 arctg( 1x ) ln( 12 x ) 2 x 2 6), 45x 24 x x2 45x 24 x 49 arcsin§¨¨  ·¸¸ © 7 7¹ x 2 7), ( 3x 2x ) 5x 24 x 3 arcsin§¨¨  ·¸¸ © 3 3¹ x x x 8), ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ¸¸·1 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 6 x x 9),  2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ·¸¸3 ©2¹ 2 § · x x x 1 x 3 10), ln¨¨§ tg§¨¨ ¸¸·3 ¸¸·8 ln¨¨ tg¨¨§ ¸¸· 6 tg§¨¨ ¸¸·13 ¸¸16 arctg¨¨§ tg§¨¨ ¸¸· ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©2 © 2 ¹ 2¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 82 (5 x ) 7x· 1), 3 ln( x )3 e 4 arctg §¨¨ ¸¸ © 2 ¹ 1 2 x3 5 x2 ( 24 x 390 x 236 x ) ln( 3 x ) 2),  x 36 9 4 3), 8 ln( arcctg ( 9 x ) ), 4), ln( x2 )3 ln( x5 )ln( 1x ) x 3 5), 2 ln( x3 )4 ln( x 26 x13 )4 arctg§¨¨  ·¸¸ © 2 2¹ §x 5 x 210 x89 ¸· 6), x 210 x89 x5 x 210 x89 64 ln¨¨   ¸ 8 ©8 8 ¹ 7), 3 ln( x5 x 210 x26 )( 5 x 23 x4 ) x 210 x26 x x x 8), ln¨§ tg¨§ ·¸3 ¸·3 ln¨§ tg¨§ ·¸1 ·¸ln¨§ tg¨§ ·¸¸2 ·¸¸ ¨ ¨ ¸ ¸ ¨ ¨ ¸ ¸ ¨ ¨ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9),  2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x 2 2 © © ¹ ¹ © © ¹ ¹ tg¨¨§ ·¸¸1 ©2¹ 2 § · x x x 1 x 2 10), 3 ln§¨¨ tg¨¨§ ·¸¸1 ·¸¸3 ln¨¨ tg§¨¨ ¸¸· 4 tg¨¨§ ¸¸·13 ¸¸2 arctg¨¨§ tg¨¨§ ·¸¸ ·¸¸ © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 83

1), 4 sin( 3 x )3 ln( x )5 cos( 2 x ) 1 1 x 2), ln( 116 x 2 ) ( 16 x 264 x1 ) arctg ( 4 x ) 4 32 8 arcsin( 5 x ) 3 3), 4 e , 4), 4 ln( x1 )3 ln( x4 ) x4 x 1 5), 8 ln( x 24 x8 )24 arctg§¨¨ 1 ·¸¸ ln( x1 ) ©2 ¹ 3 x 6), x 28 x x4 x 28 x 16 arcsin§¨¨ 1 ·¸¸ ©4 ¹ x 5 7), ( 5x 24 x ) 9x 210 x 4 arcsin¨¨§  ·¸¸ © 4 4¹ x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

4 x x 9), 6 ln¨§¨ tg¨§¨ ¸·¸4 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ·¸¸1 ©2¹ 2 § · x x x 10), 8 ln¨¨ tg¨¨§ ¸¸· 2 tg§¨¨ ¸¸·5 ¸¸2 ln¨¨§ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 84

2), e

(9 x )

( 73 x3 x 2 )

1), 2 cos( 5 x )5 ln( x )5 arcsin( 6 x )

arctg( 9 x )

3), 8 e , 4), 3 ln( x4 )2 ln( x6 )ln( x2 ) x 5), ln( 1x )6 ln( x 26 x18 )8 arctg§¨¨ 1 ·¸¸ ©3 ¹ §x 5 x 210 x61 ¸· 6), x 210 x61 x5 x 210 x61 36 ln¨¨   ¸ 6 ©6 6 ¹ 7), 2 ln( x2 x 24 x5 )( 2 x 25 x1 ) x 24 x5 x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·ln¨¨§ tg¨¨§ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 6 x 9), 2 ln§ tg§ ·3 · 6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· ¨ ¨ ¸ ¸ ¨ ¨ ¸ ¸ © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹ 2 · § x x x x 10), 2 ln¨¨ tg¨¨§ ¸¸· 6 tg§¨¨ ¸¸·10 ¸¸20 arctg¨¨§ tg§¨¨ ¸¸·3 ¸¸·2 ln¨¨§ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 85

1), arcsin( 7 x )arctg ( x )3 ln( x ) 1 5 x3 x2 ( 30 x 318 x 2108 x ) ln( 8 x ) 2),  6 x 18 9 2 arccos( 9 x ) 1 ln( x1 )3 ln( x2 ) 3), 2 e , 4),  x2 x 2 1 5), 12 ln( x 24 x13 )18 arctg§¨¨  ·¸¸ ln( 32 x ) © 3 3¹ 2 x 6), 3 6 xx 2  6 xx 2 x9 arcsin¨¨§ 1 ·¸¸ ©3 ¹ 7), ( 54 x 2x ) 8x 26 x 5 arcsin( x3 ) x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸2 ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9), 6 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ·¸¸1 ©2¹ 2 · § x x x x 10), 2 ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·5 ¸¸4 arctg¨¨§ tg§¨¨ ¸¸·2 ¸¸·3 ln¨¨§ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

(3 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 86

1), 5 e 4 cos( 2 x )3 sin( 4 x ) 1 1 3 2),  cos( 5 x ) sin( 5 x ) x sin( 5 x ) 25 5 5 3), 8 ln( sin( 2 x ) ), 4), 3 ln( x3 )ln( x6 )2 ln( x2 ) 1 x 2 ln( 23 x )12 ln( x 24 x13 )8 arctg§¨¨  ·¸¸ 3 © 3 3¹ 5),

6), x 26 x27 x3 x 26 x27 36 ln( x3 x 26 x27 ) 7), ln( x4 x 28 x15 )( 4 x 22 x3 ) x 28 x15 x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸2 ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 6 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ ¸¸ ©2¹ 2 § x x · x x 10), 4 ln¨¨ 22 tg§¨¨ ¸¸·tg§¨¨ ¸¸· ¸¸6 arctg¨¨§ tg§¨¨ ¸¸·1 ¸¸·ln¨¨§ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

( 6 x )

5 sin( 4 x )8 x

(3 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 87

1), 4 e 2), ( 63 x7 x 2 ) e arccos( 9 x ) 3 3), 4 e , 4),  3 ln( x5 )ln( x1 ) x5 5), 4 ln( x 24 x5 )12 arctg( x2 )ln( 1x ) 6), 15x 28 x x4 15x 28 x arcsin( x4 ) x 5 7), ( 12 x 23 x ) 16x 210 x 2 arcsin¨¨§  ·¸¸ © 3 3¹ x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸3 ln¨¨§ tg¨¨§ ¸¸·1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 4 x x 9), 4 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ¸¸·1 ©2¹ 2 § x x · x x 10), 2 ln¨¨ 106 tg¨¨§ ¸¸·tg§¨¨ ¸¸· ¸¸16 arctg¨¨§ tg¨¨§ ¸¸·3 ¸¸·ln¨¨§ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

1), 5 arctg ( 2 x )6 x 5 sin( x ) 1 4 x3 7 x2 ( 48 x 3126 x 2216 x ) ln( 9 x )  6 x 9 4 36

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 88

2), cos( 9 x )

3), 4 e , 4), 2 ln( 3x )3 ln( x4 )3 ln( x3 ) 3 x 5), 2 ln( 136 xx 2 )14 arctg§¨¨  ·¸¸2 ln( 1x ) ©2 2 ¹ 6), 3 556 xx 2  556 xx 2 x64 ln( x3 556 xx 2 ) 7), 3 ln( x5 x 210 x24 )( 4 x33 x 2 ) x 210 x24 x x x 8), ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ¸¸·1 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 6 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 4 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹ 2 · § x x 1 x 1 x 10), 4 ln¨¨ tg¨¨§ ¸¸· 2 tg§¨¨ ¸¸·5 ¸¸6 arctg¨¨§ tg§¨¨ ¸¸· ¸¸·ln¨¨§ tg§¨¨ ·¸¸2 ¸¸· © ©2¹ ©2¹ ¹ ©2 © 2 ¹ 2¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 89

1), 5 ln( x )4 cos( 3 x )10 x 2 2 2 2),  cos( 3 x ) sin( 3 x ) x sin( 3 x ) 9 3 3

arccos( 6 x ) 5 3), 6 e , 4), 4 ln( x3 ) 5 ln( x2 ) x2 x 3 5), 8 ln( x 28 x20 )36 arctg §¨¨ 2 ·¸¸ ln( 32 x ) ©2 ¹ 2 6), 15x 28 x x4 15x 28 x arcsin( x4 ) 7), ( 2 x33 x 2 ) 3x 24 x 5 arcsin( x2 ) x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸3 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9), 4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg§¨¨ ¸¸·1 ©2¹ 2 · § x x 1 x 3 x 10), 4 ln¨¨ tg¨¨§ ¸¸· 6 tg§¨¨ ¸¸·13 ¸¸4 arctg¨¨§ tg§¨¨ ¸¸· ¸¸·ln¨¨§ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ ©2 © 2 ¹ 2¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 90

3x· 1), 2 arcsin¨¨§ ¸¸2 arctg ( 3 x )cos( 5 x ) © 2 ¹ (7 x ) 2), ( 19 x3 x 2 ) e

cos( 8 x )

3), 8 e , 4), 2 ln( x4 )ln( x3 )2 ln( 1x ) x 3 5), ln( 3x )8 ln( x 26 x13 )20 arctg¨¨§  ·¸¸ © 2 2¹ §x 1 x 24 x20 ¸· 6), x 24 x20 x2 x 24 x20 16 ln¨¨   ¸ 4 ©4 2 ¹ 7), 2 ln( x1 x 22 x )( 4 x 23 x4 ) x 22 x x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ ¸¸ ©2¹ 2 § x x x · x 10), 2 ln§¨¨ tg§¨¨ ¸¸·3 ¸¸·2 ln¨¨ 22 tg§¨¨ ¸¸·tg¨¨§ ¸¸· ¸¸8 arctg¨¨§ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 91

1), 3 ln( x )3 arcsin( 7 x )3 sin( x ) 1 7 x3 9 x2 ( 84 x 3162 x 236 x ) ln( 6 x ) 2),  x 36 9 4 arccos( 2 x ) 5 3), 2 e , 4), 3 ln( 3x )2 ln( x3 ) 3x 5), 4 ln( x 28 x17 )34 arctg( x4 )2 ln( 1x ) x 1 6), 15x 22 x x 15x 22 x 16 arcsin§¨¨  ·¸¸ © 4 4¹ x 7), ( 5 x 24 x4 ) x 24 x 4 arcsin§¨¨ 1 ·¸¸ ©2 ¹ x x x 8), 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸3 ln¨¨§ tg¨¨§ ¸¸·2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 4 x 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· 4 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹

2

§ x x · 1 x x 10), 3 ln¨¨ 186 tg¨¨§ ¸¸·tg§¨¨ ¸¸· ¸¸2 arctg§¨¨ tg§¨¨ ¸¸·1 ¸¸·ln¨¨§ tg§¨¨ ¸¸·3 ¸¸· © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 92

3x· x 1), 3 cos( 4 x )4 arcsin¨§ ¨ ¸¸e © 2 ¹ 1 1 2),  cos( 3 x )sin( 3 x ) x sin( 3 x ) 3 3

arctg( 3 x )

3), 4 e , 4), 2 ln( x3 )ln( x1 )2 ln( x2 ) x 2 3 5), 12 ln( x 24 x13 )12 arctg§¨¨  ·¸¸ ln( x1 ) © 3 3¹ 2 6), x 210 x x5 x 210 x 25 ln( x5 x 210 x )

7), 2 ln( x5 x 210 x26 )( 2 x 23 x1 ) x 210 x26 x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 4 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 § · x x 1 x x 10), 6 ln¨¨ tg¨¨§ ¸¸· 6 tg§¨¨ ¸¸·18 ¸¸8 arctg¨¨§ tg§¨¨ ¸¸·1 ¸¸·2 ln¨¨§ tg§¨¨ ¸¸·2 ¸¸· © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹ © ©2¹ ¹

1), 10 x 2 e ( 4 x )

2 ln( x )

( x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 93

2), ( 93 x8 x 2 ) e sin( 3 x ) 4 3), 4 e , 4), 5 ln( 3x ) 4 ln( x1 ) 3x 1 5), 4 ln( 106 xx 2 )28 arctg ( 3x ) ln( x1 ) 2 x 4 6), 7x 28 x x4 7x 28 x 9 arcsin§¨¨  ·¸¸ © 3 3¹ x 5 7), ( 33 x 2x ) 16x 210 x 3 arcsin¨¨§  ·¸¸ © 3 3¹ x x x 8), ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 6 9), 4 ln¨§¨ tg¨§¨ ¸·¸3 ¸·¸2 ln¨§¨ tg¨§¨ ¸·¸3 ¸·¸ © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 · § x x x x 10), ln¨¨ tg¨¨§ ¸¸· 4 tg§¨¨ ¸¸·5 ¸¸8 arctg¨¨§ tg§¨¨ ¸¸·2 ¸¸·3 ln¨¨§ tg§¨¨ ·¸¸3 ·¸¸ © ©2¹ ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ (3 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 94

1), 5 sin( x )5 e 3 cos( 3 x ) 1 5 x2 2), ( 12 x 310 x 220 x ) ln( 4 x )x 3 5 x 4 4 3), 6 sin( 4 x ) , 4), ln( x3 )3 ln( x6 )2 ln( 1x ) 3 x 5),  ln( 1x )3 ln( x 26 x18 )2 arctg§¨¨ 1 ·¸¸ 2 ©3 ¹ 6), x 210 x26 x5 x 210 x26 ln( x5 x 210 x26 )

7), 4 ln( x3 86 xx 2 )( 24 x2 x 2 ) 86 xx 2 x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸3 ¸¸·ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 4 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸· 2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·3 ¨¨ ¸¸ ©2¹ 2 § · x x 1 x 2 x 10), 12 ln¨¨ tg§¨¨ ·¸¸ 4 tg§¨¨ ·¸¸13 ¸¸8 arctg¨¨§ tg§¨¨ ¸¸· ¸¸·3 ln§¨¨ tg§¨¨ ·¸¸2 ¸¸· © ©2¹ ©2¹ ¹ ©3 © 2 ¹ 3¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 95

7x· 1), 5 arcsin( 4 x )4 cos( 2 x )arctg§¨¨ ¸¸ © 3 ¹ ( 3 x6 ) 19 x 2 § 1 2), ¨¨ x x 2 ·¸¸ arcsin( 3 x ) 18 18 © ¹ 4 3), 6 sin( 3 x ) , 4), ln( 3x ) 3 ln( x1 ) 3x x 3 5), 8 ln( x 24 x8 )20 arctg §¨¨ 1 ·¸¸ ln( 32 x ) ©2 ¹ 2 x 6), x 28 x x4 x 28 x 16 arcsin§¨¨ 1 ·¸¸ ©4 ¹ x 5 7), ( x3x 2 ) 9x 210 x 2 arcsin¨¨§  ·¸¸ © 4 4¹ x x x 8), 2 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·3 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x x 6 9), 6 ln¨¨§ tg¨¨§ ¸¸·3 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· © ©2¹ ¹ tg§ x ·3 © ©2¹ ¹ ¨¨ ¸¸ ©2¹ 2 · § x x x 1 x 10), 3 ln§¨¨ tg§¨¨ ¸¸·3 ¸¸·3 ln¨¨ tg¨¨§ ¸¸· 6 tg§¨¨ ¸¸·18 ¸¸8 arctg¨¨§ tg§¨¨ ·¸¸1 ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ ©3 © 2 ¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 96

2), 3 e

( 4 x )

( 3xx 2 )

1), 3 ln( x )2 cos( x )3 sin( 3 x )

arccos( 7 x )

3), 8 e , 4), 2 ln( x5 )ln( x1 )ln( x2 ) x 1 5), 6 ln( 186 xx 2 )20 arctg §¨¨ 1 ·¸¸ ln( 1x ) ©3 ¹ 2 6), x 28 x20 x4 x 28 x20 36 ln( x4 x 28 x20 ) 7), 5 ln( x3 86 xx 2 )( 12 x5 x 2 ) 86 xx 2 x x x 8), ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 2 x x 9),  4 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸·2 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ¸¸·2 ©2¹ 2 · § x x 1 x 3 x 10), 4 ln¨¨ tg¨¨§ ¸¸· 6 tg§¨¨ ¸¸·13 ¸¸8 arctg¨¨§ tg§¨¨ ¸¸· ¸¸·3 ln§¨¨ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ©2¹ ¹ ©2 © 2 ¹ 2¹ © ©2¹ ¹

1), 2 arcsin ( 6 x )2 sin( x )2 cos( 2 x )

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 97

2

2§ 21 21 x x ·  ¸¸ x 2),  ¨¨ §¨¨ 6 xx 2 ·¸¸ ln( 7 x )6 3 ©© 4 8 3 ¹ ¹ 4 3), 2 arcctg ( 8 x ) , 4),  2 ln( x3 )3 ln( x2 ) x2 5), ln( x 28 x17 )10 arctg( x4 )ln( 1x ) x 5 6), 9x 210 x x5 9x 210 x 16 arcsin¨¨§  ·¸¸ © 4 4¹ x 3 7), ( 4 x13 x 2 ) 7x 26 x 5 arcsin§¨¨  ·¸¸ © 4 4¹ x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸3 ·¸¸2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 2 x 9), 4 ln¨¨§ tg¨¨§ ¸¸·4 ¸¸· 4 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨¨ ¸¸ ©2¹ 2 § x x x · x 10), 2 ln§¨¨ tg§¨¨ ¸¸·3 ·¸¸2 ln¨¨ 106 tg¨¨§ ·¸¸tg¨¨§ ¸¸· ¸¸14 arctg¨¨§ tg§¨¨ ¸¸·3 ¸¸· © ©2¹ ¹ © ©2¹ ©2¹ ¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 98

7x· §7x· 1), 4 arctg¨¨§ ¸¸2 sin( 2 x )2 arcsin¨¨ ¸¸ © 3 ¹ © 3 ¹ 2 2 2 2),  sin( 5 x ) cos( 5 x ) x cos( 5 x ) 25 5 5 3), 6 ln( arctg ( 8 x ) ), 4), ln( x4 )ln( x3 )2 ln( x2 ) 3 5), 4 ln( 106 xx 2 )28 arctg( 3x ) ln( 32 x ) 2

2

6), x 26 x8 x3 x 26 x8 ln( x3 x 26 x8 ) 7), ln( x3 x 26 x8 )( x 24 x4 ) x 26 x8 x x x 8), 2 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ·¸¸1 ·¸¸ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ x 6 x 9), 6 ln¨¨§ tg¨¨§ ¸¸·2 ¸¸· 6 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· © ©2¹ ¹ © ©2¹ ¹ tg§ x ·1 ¨ ¸ ¨ ¸ ©2¹ · § §x· · §3 1 § x ·· ¸ ¸2 arctg¨¨ 22 tg¨¨ 2 ¸¸ ¸¸3 ln¨¨ tg¨¨ 2 ¸¸2 ¸¸ ¹ © © ¹¹ © © ¹ ¹

§ x x 10), 2 ln¨¨ 136 tg¨¨§ ¸¸·tg§¨¨ ¸¸· © ©2¹ ©2¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 99

4x· 1), 4 sin( 4 x )5 arctg ¨¨§ ¸¸4 x © 3 ¹ ( 7 x ) 2), ( 54 x9 x 2 ) e 5 3), 8 arctg( 3 x ) , 4), 3 ln( x2 ) 2 ln( 1x ) 1x 1 x 5),  ln( 12 x )4 ln( x 24 x8 )12 arctg§¨¨ 1 ·¸¸ 2 ©2 ¹ x 2 6), 21x 24 x x2 21x 24 x 25 arcsin§¨¨  ·¸¸ © 5 5¹ x 4 7), ( 22 x 23 x ) 7x 28 x 3 arcsin§¨¨  ·¸¸ © 3 3¹ x x x 8), ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·ln¨¨§ tg¨¨§ ¸¸·1 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ·¸¸ © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹

x x 6 9), 2 ln¨§¨ tg¨§¨ ¸·¸4 ¸·¸4 ln¨§¨ tg¨§¨ ¸·¸1 ¸·¸ © ©2¹ ¹ tg§ x ·1 © ©2¹ ¹ ¨¨ 2 ¸¸ © ¹ 2 § · x x 1 x 1 x 10), 8 ln¨¨ tg¨¨§ ¸¸· 2 tg§¨¨ ¸¸·5 ¸¸12 arctg¨¨§ tg§¨¨ ¸¸· ¸¸·2 ln§¨¨ tg§¨¨ ¸¸·1 ¸¸· © ©2¹ ©2¹ ¹ ©2 © 2 ¹ 2¹ © ©2¹ ¹

______________________________________________________ ȼɚɪɢɚɧɬ ʋ 100

(5 x ) 7x· 1), 2 e 2 x 2 arcsin§¨ ¸ ¨ ¸ © 3 ¹ 1 5 x3 9 x2 ( 60 x 3162 x 2252 x ) ln( 4 x ) 2),  7 x 36 9 4 3), 8 ln( arccos ( 9 x ) ), 4), ln( x2 )ln( x6 )ln( 1x ) x 1 5), 12 ln( 102 xx 2 )12 arctg§¨¨  ·¸¸2 ln( 1x ) © 3 3¹ 6), x 26 x7 x3 x 26 x7 16 ln( x3 x 26 x7 ) 7), 4 ln( x1 22 xx 2 )( 4 x 23 x2 ) 22 xx 2 x x x 8), 3 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸1 ¸¸·3 ln¨¨§ tg¨¨§ ·¸¸2 ¸¸· © ©2¹ ¹ © ©2¹ ¹ © ©2¹ ¹ 6 x x 9), 4 ln¨§¨ tg¨§¨ ¸·¸2 ¸¸·4 ln¨¨§ tg¨¨§ ¸¸·1 ¸¸· x © ©2¹ ¹ © ©2¹ ¹ tg¨¨§ ·¸¸1 ©2¹ 2 · § x x x 10), 12 ln¨¨ tg¨¨§ ¸¸· 2 tg§¨¨ ¸¸·10 ¸¸ln¨¨§ tg§¨¨ ·¸¸2 ¸¸· © ©2¹ ©2¹ ¹ © ©2¹ ¹