ИДЗ по матану

Индивидуальные задания по теме «Неопределенные интегралы»

Вариант 1

1.

ex 3 4 ex dx

2.

tg x

dx

cos2 x

3.

1 x2 x dx

1 x4

4.

2

dx

x2 2x 5

5.

x

dx

x2

3x 10

6.

(4 3x)e 3xdx

7.

x3 1

dx

x2 x

8.

1

dx

(x 1)(x2 8)

9.

x 2

dx

3 (x

2)2 (x

2)3

10.

x2 8

dx

x

4

11.

1

dx

cos3 xsin x

12.

1

dx

3 5sin x 3cos x

Вариант 2

1.

x2

ln x2

dx

x

2.

x5

dx

x6 7

2x

3.

arcsin x

dx

1 x2

4.

1

dx

x2

4x

3

5.

3x 2

dx

x2

2x 5

6.(x2 x 1)ln x dx

7.3x3 1 dx

x2 1

8.				2x 3					dx
		(x 1)2 (x2 4)
9.		arctg x
								dx
				(1 x)
			x
10.			x4
						dx
		1 x2

11. sin3 x dx cos4 x

1

12. 3sin x 2cos x dx

41

Вариант 3

1.

(arccos x)3

1

dx

1 x2

2.

2x 3

dx

(x2 3x 1)4

3.

5x 1

dx

4 x2

3

4.

dx

x2 4x 8

5.

3x 2

dx

x2 x

2

6.

(3x 4)e3xdx

7.

x3 17

dx

x2 4x 3

8.

5x 8

dx

x3 4x2 4x

x

9. 1 x3 dx

10. x3 1 x2 dx

11. cos 4x dx sin4 2x

1

12. 5 4sin x 3cos x dx

Вариант 4

1.

tg(x 1)

dx

cos2 (x 1)

7

x

2.

dx

x

1 x x

2

3.

dx

3

1 x2

4.

4

dx

x2

2x 2

5.

4x 1

dx

x2

x 1

6.(4x 2)cos 2x dx

7.

2x3 5

dx

x2 x 2

8.

1

dx

x2 (x 1)2

9.

1

dx

x 3

x

10.

x2 1

dx

x

2

11.

sin3 x

dx

cos x

12.

1

dx

5 3cos x

42

Вариант 5

1.

e

2 x 1 3

dx

2x 1

2.

1

dx

arccos x

1 x2

3.

4

4 9x2

dx

4 9x

2

4.

1

dx

x2

2x 8

1 2x

5. dx

x2 2x 3

6.(4 16x)sin 4x dx

7.		2x3 1	dx
		x2 x 6 x2

8.x4 2x2 4 dx

x3 1

9.			1 3 x 1
							dx
				3
			x 1		x 1

10.x2 9 dx

x4

	1
11.					dx
			sin4 x cos2 x
	1
12.					dx
			sin2 x tg 2 x

Вариант 6

1.

sin x cos x

dx

(cos x sin x)5

2.

ex

dx

e2 x

9

3.

x2 x 1

dx

x2

3

1

4.

3

dx

9x2 12x 5

5.

3x 2

dx

x2 2x 4

6.

(5x 2)e3xdx

7.

3x3 25

dx

x2 3x 2

8.

3x2 x 2

dx

x3 2x2 4x 8

9.

x

dx

1

4 x3

10.

1

dx

x2

1 x2

11.

sin x cos x

dx

cos4 x 5

12.

1

dx

5cos x

3

43

Вариант 7

1.x3 x dx

x4 1

1

x

2.

e

dx

x2

3.

arctg x 3x

dx

1 x

2

4.

1

dx

x2 4x

5

5.

x

dx

x2

4x 5

6.

(1 6x)e2xdx

7.

x3 2x2 3

dx

(x 1)(x 2)(x 3)

8.

x5

dx

16 x4

9.

x

dx

3

x 1

x 1

10.

1

dx

x4

(4 x2 )5

1

11.

dx

tg8 x

12.

1

dx

1 sin2 x

Вариант 8

1.1 ln2 (x 1) dx

x1

2.

3x2

2x 7

dx

x3 x2 7x 2

3.

3 2ctg2 x

dx

cos

2

x

4.

3

dx

x2 4x

x1

5.5x2 2x 1 dx

6.x ln(x2 1) dx

7.

3x3 2x2 1

dx

(x 2)(x 2)(x 1)

8.

x2 2

dx

(x 1)(x 1)2

9.

3 x

dx

x(

3

)

x

x

10.

x2 4

dx

x

11.

tg2 x

dx

cos4 x

12.

1

dx

3sin2 x 5cos2 x

44

Вариант 9

1.

4arctg x x

dx

1 x

2

2.

e x3 x2dx

3.

x3 x

dx

1 x4

4.

2

dx

4x2 4x 5

5.

x

dx

x2 x 1

6.

(4x 3)sin 5x dx

7.

x3

dx

(x 1)(x 1)(x 2)

8.

x

dx

(x 1)2 (x2 1)

3

9.

x

dx

3 x2

x

10.

9 x2

dx

x

11.

cos x

dx

(1 cos x)2

12.

1

dx

1 sin x

Вариант 10

1.

x cos x

dx

x2

2sin x

2.

x2

dx

x6 4

3.

1

1 4x2

dx

1 4x

2

4.

1

dx

x2

6x 13

5.

x 4

dx

x2 x 2

6.(2 4x)sin 2x dx

7.

x3 3x2 12

dx

(x 4)(x 3)(x 2)

8.

x4 2

dx

x4 x3 2x2

9.

6 x

dx

1 3

x

10.

x2

dx

1 x2

11.

sin6 x

dx

cos4 x

1

12.

dx

5 2sin x cos x

45

Вариант 11

1.

(arcsin x)2

1

dx

1 x2

2.

x

dx

x4

1

3.

ln x

dx

x

1 ln2

x

4.

1

dx

3x2

6x 4

5.

x

dx

x2 5x 4

6.

x2 arctg x dx

7.

x3 3x2 12

dx

(x 4)(x 3)x

8.

x2 4x 4

dx

x(x 1)2

9.

1

dx

x

e2

ex

10.

1

dx

x

9 x2

11.

sin2 x cos3 x dx

12.

1

dx

4 5sin2

x 3cos2 x

Вариант 12

1.

2cos x 3sin x

dx

(2sin x 3cos x)3

2.

7x 2

dx

x2 10

3.

2x arccos3x 2

dx

1 9x2

4.

1

dx

x2

4x 1

5.

2x 1

dx

5x2 2x 1

6.

(4x 3)e 2xdx

7.

4x3 x2 2

dx

x(x 1)(x 2)

8.

2x 5

dx

x3 x2 2x 2

9.

1

dx

1 2x 4 1 2x

10.

x2 5

dx

x

2

11.

1 tg x

dx

sin 2x

12.

1

dx

1 3cos2 x

46

Вариант 13

1.

x

dx

x4 1

2.

(8cos

x

5)2 sin

x

dx

3

3

3.

8x arctg 2x

dx

1 4x

2

4.

1

dx

x2 2x 2

5.

x 6

dx

x2 2x 17

(

8x)sin 3x dx

6.

2

7.

3x3 2

dx

x3 x

8.

3x2 4

dx

(x 7)(x2

2x 1)

1 4

9.

x

dx

x

x

10.

x5

dx

1 x2

11.

tg7 x dx

12.

1

dx

4sin2 x 9cos2 x

Вариант 14

1.

x cos x sin x

dx

(xsin x)2

2.

ln x

dx

x

3.

9

9 x2

dx

9 x

2

4.

1

dx

x2 3x 10

5.

5x 3

dx

x2

4x 5

6.(x2 2x 3) ln x dx

7.

x3 3x2 12

dx

(x 4)(x 2)x

8.

x4 1

dx

x3 4x

9.

1

dx

(x

1)3

x 1

10.

x2 4

dx

x

3

11.

sin 2x

dx

cos7 x

12.

2 sin x

dx

2 cos x

47

Вариант 15

1.

x2 1

dx

(x3 3x 1)5

2.

sin x

dx

4 cos2 x

3.

x

1 x2

dx

x2

3

1

4.

1

dx

x2 x 1

5.

4x 3

dx

x2 2x 6

6.

(5x 6)cos 2x dx

7.

x5 x3 1

dx

x2 x

8.

x4 3x3 3x2 5

dx

x3 3x2 3x 1

9.

1

dx

1 ex

10.

x2

dx

(1 x2 )5

1

11.

dx

cos4 x

12.

1

dx

3sin2 x 2cos2 x

Вариант 16

1.8x arctg 2x dx

14x2

2.cos11 2x sin 2x dx

3.		2	x 3		dx
		1 x2

1

4. x2 x 12 dx

	5.			4x		dx
			x2	2x 3

6.xsin x cos x dx

7.x5 3x3 1 dx

x2 x

8.	2x 5	dx
	(x2 5x 4)3

1

9. 3x ( 3x 1) dx

10.					1					dx
				x3 x2				1
11.					1						dx
				sin4 x cos4 x
12.					1			dx
			2		cos x

48

Вариант 17

1.				4 ln 2x		dx
				x
2.			cos x
					dx
		sin2 x

3.41 x2 3x2 dx

x2 1

4.										4										dx
				x2 10x 29
5.								3x 4															dx
							x2							6x				8
6.	x arcsin												1				dx
														x
7.				2x5					8x3 3											dx
							x		2	2x
8.				x4 2x3 3x 4																					dx
										x	3			1
9.				1												dx
							x 4					x
10.					9 x2									dx
							x		2
11.	sin4 x cos2 x dx
12.											1												dx
					sin6 x cos6 x

Вариант 18

1.

sin x 1

dx

3 3 cos x x

2.

x 8

dx

x2

3

3.

x arctgx 4

dx

1 x

2

4.

1

dx

x2

18x 80

5.

8x 11

dx

x2 2x 5

6.x ln(x2 1) dx

7.3x5 12x3 7 dx

x2 2x

8.			x2 5x 2										dx
			(x2 1)(x 1)
9.			1									dx
				x (1 3 x )
10.			1							dx
	x4 x2						3

11. sin3 x dx cos4 x

sin 2x

12. sin4 x cos4 x dx

49

Вариант 19

1.

1

dx

cos2 x (3 tg x 1)

2.

x

dx

x4

4

x

3.

1 x4

1 x

dx

1 x2

4.

1

dx

9x2 12x 2

5.

2 5x

dx

4x2 4x 2

6.

x ln2 x dx

7.

x5 9x3 4

dx

x

2

3x

8.x4 1 dx

x4 1

9.							1				dx
			3 (2x			1)2				2x 1
10.				x2 4			dx
				x	3
11.	sin4 x cos5 x dx
12.			sin2 x					dx
			1 sin2 x

Вариант 20

1.

(arccos3x)4

x

dx

1 9x2

x2

2.

1 x3 dx

3.

2 3tg2 x

dx

sin2

x

4.

1

dx

x2

2x 3

5.

x

dx

9x2 12x 2

6.

(2 3x)cos 4x dx

7.

x5 25x3 1

dx

x

2

5x

8.

2x 1

dx

(x2 2x 5)2

x 3

9.

2 x dx

10.

1

dx

x4

1 x2

11.

sin4 x

dx

cos2 x

12.

1

dx

sin2 x 4cos2 x

50