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Башкирский Государственный Аграрный Университет

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Математика. Интегральное исчисление функций одной переменной. Практикум

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<<< < Предыдущая 1 2 3 4 5 6 78 / 178 9 10 11 12 13 14 15 16 17 > Следующая >>>

9.5. (3x 2)sin 3x dx .

9.7. x2 x dx .

9.9. ( 5x)cos x dx .

9.11. (2 3x)e x/ 2 dx .

9.13. (3 x)sin x dx .

9.15. (1 2x)

5 x dx .

9.17. (x 5)cos7x dx .

9.19. (2x 7)e 4 x dx .

9.21. ( / 2 2x) sin 3xdx .

9.23. (5x 1)7x dx .

9.25. (2x )cos 3x dx .

9.27. (2 3x)e 6 x dx .

9.29. (2 9x) sin 32x dx .

9.6. x arctg x dx .

9.8. (x2 x)log3 x dx .

9.10. (x2 2x 4)ln x dx .

9.12. arcsin x dx .

9.14. arcctg x dx .

9.16. (x2 x 4)log4 x dx .

9.18. (x 2)ln x dx .

9.20. (1 x)arcctg x dx .

9.22. arcsin 3x dx .

9.24. (x3 x)log2 x dx .

9.26. x4 ln x dx

9.28. (x 2)arctg 2x dx .

9.30. arccos5x dx .

Задача 10

10.1. ln2 x dx . x3

10.3. xarcctg2 2x dx .

10.5. ln2x x dx .

10.7. (x2 2x 5)sin 2xdx .

10.9. ln2 2x dx .

10.11. lgx22 x dx .

10.13. x arctg2 x dx .

10.15. (x3 x)cos xdx .

10.17. (x 1)ln2 (x 1) dx .

10.19. (4 x2 )5x dx .

10.21. lnx25x dx .

10.23.

x 2 ln2 (x 2) dx .

10.25. ln2 (x 4)dx .

10.27. x arcctg2 xdx .

10.29. x arccos2 x dx .

10.2. x3e x2 dx .

10.4. (x2 2x)cos x dx .

10.6. x5 sin x3dx .

10.8. x2e 5xdx .

10.10. x2 cos2 x dx .

10.12. (1 x2 )e2 x dx .

10.14. ln(x2 1) dx .

10.16. (x 2 x2 )e 3x dx .

10.18. (x2 2x)sin2 x dx .

10.20. ln(x2 9) dx .

10.22. x2 sin x cos x dx .

10.24. arcsin2 x dx .

10.26. (x2 x)sin 3x dx .

10.28. (x2 3x3 )ex dx .

10.30. x3 sin x dx .

arctg x

Задача 11

11.1. arcsin				x dx .
			1 x
11.3.	x ln xdx
					.
	(x	2	1)	2

11.5.3x dx .

11.7. x arcsin x dx . (1 x2 )3

11.9. x arctg x dx . 1 x2

11.11. x arctg x dx . (1 x2 )2

11.13. x tg2 xdx .

11.15. arctg		2x 1dx .
11.17.	x ln xdx			.
	2		3
	(x	1)

11.19.arcsin x dx .

11.21.arctg x dx .

11.23. arctg(1 x)dx .

11.25. arctg 1x dx .

11.2. arctg x xdx .

11.4.arctg x dx .

11.6. e2 x cos x dx .

11.8. x cos x dx . sin2 x

11.10. x2 (x2 1)dx .

11.12.	xex		dx .
	1 e	x

11.14. e 3x sin 2x dx .

11.16. cosxsin3 xx dx .

11.18. (1arctgx)x3 dx .

11.20. cosln x dx .

11.22. e3 x dx

11.24. sin x dx .

11.26. arcsin(x / 2) dx . 2 x

11.27. x ln							1 x dx .
							1 x
11.29.							x2							dx .
11.29.			4 x2									3		dx .
			4 x2
Задача 12
12.1.						x2										dx .
12.1.	x		2		2x								2			dx .
	x				2x								2
12.3.							xdx														.
12.3.			x		2		2x 2														.
			x				2x 2
12.5.						x dx											.
12.5.			2 x x											2			.
			2 x x
12.7.						xdx													.
12.7.			x		4		x				2	1							.
			x				x					1
12.9.											dx													.
12.9.	x				ln			2		x														.
	x				ln					x	4ln x 7
12.11.							ex dx													.
12.11.			e	2 x			e				x		9							.
			e				e						9
12.13.						x2 1												dx .
12.13.			x	2		2x									5			dx .
			x			2x									5
12.15.					(2				x)dx													.
12.15.					2																	.
					x				6x 5
12.17.					(x 2)dx																		.
12.17.					3 6x x														2				.
					3 6x x
12.19.							(ln x 1)dx																		.
12.19.		x(ln					2		x				2ln x 10)												.
		x(ln							x				2ln x 10)
12.21.				x2 8															dx .
12.21.			x	2											5				dx .
			x			6x									5

11.28.	x cos x				dx .
	sin		3	x

11.30.	x ln xdx
							.
	(x	2	9)			2

12.2.			2x dx					.
12.2.	2	2 x		2	x	1		.
	2			2		1
12.4.				(ln x 1)dx								.
12.4.	x		2ln x ln						2	x 8		.
	x		2ln x ln							x 8
12.6.				cos xdx							.
12.6.	sin		2	x 5sin x 2							.
	sin			x 5sin x 2
12.8.				xdx					.
12.8.		1	4x x				2		.
		1	4x x

2x 5 dx

12.10.3x2 3x 15 .


12.12.		(2x	5)dx							.
12.12.		2								.
		9x	6x 2
12.14.			sin x									dx .
12.14.		8cos x cos							2			dx .
		8cos x cos									x
12.16.		xdx				.
12.16.		3 2x x			2	.
		3 2x x
12.18.		x2 2x		dx .
12.18.	4	2		dx .
	4	4x x
12.20.		(x 1)dx						.
12.20.		2						.
		x 2x 2
12.22.		(4 3x)dx					.
12.22.		2					.
		4 6x x

12.23.

ex dx

12.24.

4 x2

dx .

8 e

2 x

2x 3

12.25.

ln x dx

12.26.

xdx

x(ln

x 12ln x 40)

4x 3 x

12.27.

5 x

dx .

12.28.

sin x

dx .

cos

4cos x 3

12.29.

2x dx

12.30.

5x 3

dx .

x 1

6x x

Задача 13

13.1.

4x3 6x2 2

dx .

13.2.

x5 8

dx .

13.3.

2x4 14x3 13x

2 7x 3

dx .

13x 10

13.4.

2x3 6x2 8x 9

dx .

13.5.

x4 6x3

13x

dx .

13.6.

3x4 8x3 27x2 33x 26

dx .

6x 8

13.7.

5x3 5x2 4x 8

dx .

13.8.x5 5x4 3 5x3 2 9x2 7x 8 dx .

x3x 2x

13.9.x4 x3 x32x2x 3x 1 dx .

13.10. 2x4 22x2 27x 27 dx . x3 9x

13.11. 2x4 3x3 11x2 7x 6 dx . x3 x2 6x

13.12. 9 3x4 11x3 13x dx . x3 4x2 3x

13.13. x5 3x4 13x3 15x2 19x 15 dx . x3 2x2 15x

13.14. x4 2x3 3x2 11x 9 dx . x3 4x2 x 4

13.15. x4 4x33 102x2 27x 24 dx . x x 12x

13.16. 2x4 8x3 4x2 14x 16 dx . x3 5x2 x 5

13.17. x4 7x3 5x2 46x 80 dx . x3 3x2 4x 12

13.18. x4 3x3 12x2 18x 12 dx . x3 2x2 3x

13.19. x4 4x3 38x2 15x 18 dx . x 9x

13.20. 3x4 x3 345x2 16x 16 dx . x 16x

13.21. 2x4 3x3 347x2 50x 100 dx . x 25x

13.22. x4 10x3 37x2 51x 17 dx . x3 6x2 11x 6

13.23.3x4 2x3 3 6x2 17x 2 dx .

13.24.

14x3 15x2 34x 30

dx .

13.25.

4x5

21x4 x3 x2 4x 42

dx .

21x

13.26.

3x3 8x2 43x 64

dx .

14x

13.27.

41x3 114x 108

dx .

36x

13.28.

3x4 2x3 34x2 73x 24

dx .

12x

13.29.

x3 3x2 2

dx .

13.30.

4x3 6x2 10x 23

dx .

Задача 14

14.1.

dx .

14.2.

2x4 8x3 x2 x

dx .

14.3.

3x2

dx .

14.4.

x3 2

dx .

(x 7)(x

2x 1)

(x 1)

14.5.

2x2 3x

dx .

14.6.

x4 2x3 x2 2x 1

dx .

(x 1)

14.7.

14.8.

dx .

2x 1)

14.9.

11x 16

dx .

14.10.

4 4x 4x2

dx .

(x 1)(x 2)

14.11.

2x3 4x2 6x 5

dx .

14.12.

3x3 5x2 7x 3

dx .

14.13. x3 6x2 10x 352 dx . (x 2)(x 2)

14.14. 2x4 13x3 16x2 27x 54 dx . (x 3)3 x2

5x2 6x 5 5x 8

14.15.(x 3)2 (x 1)2 dx . 14.16. x3 4x2 4x dx .


14.17.	2x3	6x2	7x 4		dx . 14.18.	x4 12x2 24x 27				dx .
14.17.	(x 2)(x 1)			3	dx . 14.18.	(x	2	9)	2	dx .
	(x 2)(x 1)					(x		9)


14.19.		2x3 16x2 37x 32																						dx .
14.19.							x(x							2)			3							dx .
							x(x							2)
14.20.		5x4 6x3 3x2 4x 2																							dx .
14.20.								x	3		(x 1)								2						dx .
								x			(x 1)
14.21.		9x2 4x 12													dx .											14.22.
14.21.				x	4	(x 3)									dx .											14.22.
				x		(x 3)
14.23.	14x3					2x4 8x2 5x 50																				dx .
14.23.								x		3		(x		5)						2						dx .
								x				(x		5)
14.24.		27x x3 2x2 27																					dx .
14.24.						(x					3)		3	x		2							dx .
						(x					3)			x
		x	4					3	18x											9
14.25.		x				6x			18x											9		dx .				14.26.
14.25.						2			2													dx .				14.26.
			(x 1)						(x 3)
14.27.		2x3				24x 8												dx .								14.28.
14.27.		(x		1)			2	(x 2)								2		dx .								14.28.
		(x		1)				(x 2)
14.29.		x3		4x2						7x									5		dx .					14.30.
14.29.										3											dx .					14.30.
			(x 1)(x 2)

Задача 15

16x 16 x4 2x3 x2 dx . x2 (x 2)3

5x4 3x3 7x2 8x 4dx . x3 (x 1)2

2x3 6x2 7x3 1dx . (x 1)(x 1)

5x4 3x3 4x2 5x 2dx . x3 (x 1)2

15.1.	3x 1					dx .	15.2.			dx			.
	(x 1)	2	(x	2	4)			x	2	(x	2	9)

15.3.	7x2				x3 4x 22																					dx .
15.3.		(x		2				1)(x									2	4)								dx .
		(x						1)(x										4)
15.5.			dx													.
15.5.	x	2	(x			2			4)							.
	x		(x						4)
15.7.	3x3			6x2 5x 1																					dx
15.7.		(x						1)			2	(x				2					2)				dx
		(x						1)				(x									2)
15.9.	24 33x 4x2 x3																										dx .
15.9.		(x			2				3)(x												3)		2				dx .
		(x							3)(x												3)
15.11.		x3		5x2 5x 10																							dx .
15.11.							(x				2	5)x									2						dx .
							(x					5)x
15.13.			4x2 14x 8																				dx .
15.13.		(x		2			9)(x 1)															2	dx .
		(x					9)(x 1)
15.15.		2x3 3x2 4x 28																											dx .
15.15.		(x		2			4)(x										2		4x								4)		dx .
		(x					4)(x												4x								4)
15.17.				(x 3)dx																			.
15.17.		(x						1)			2	(x				2					1)		.
		(x						1)				(x									1)
15.19.		3x3 6x2 14x 29																											dx .
15.19.				(x					2		4)(x									2		5)							dx .
				(x							4)(x											5)
15.21.		x3		2x2 35x 27																								dx .
15.21.			(x					2		2)(x 3)														2				dx .
			(x							2)(x 3)
15.23.		2x3 4x2 6x 5																									dx .
15.23.			(x				2			1)(x								2		2)							dx .
			(x							1)(x										2)
15.25.		x3 7x2 43x 23																											dx .
15.25.			(x 1)											2		(x			2		25)								dx .
			(x 1)													(x					25)
15.27.		x3		4x2 27x 3																							dx .
15.27.			(x 5)										2		(x			2			4)						dx .
			(x 5)												(x						4)

15.29. x3 8x2 x 12 dx . (x2 9)(x 1)2

15.4.	x3				6x2 8x 8
																							dx .
	(x				2		4)(x 2)													2			dx .
	(x						4)(x 2)
15.6.			3x2 x 46																		dx .
15.6.	(x			2				9)(x							1)			2			dx .
	(x							9)(x							1)
15.8.		6x2 2x 12																			dx .
15.8.	(x			2				9)(x							1)			2			dx .
	(x							9)(x							1)
15.10	3x3 8x2 13x 17																									dx .
15.10				(x			2		4)(x 3)													2				dx .
				(x					4)(x 3)
15.12.			8x2					3x3 12x 37																					dx .
15.12.						(x			2		9)(x						2			4)									dx .
						(x					9)(x									4)
15.14.			5x3 4x2 15x 11
15.14.			(x			2				4)(x				2					2x						1)			dx .
			(x							4)(x									2x						1)
15.16.			2x3					4x2 8x 18																			dx .
15.16.					(x			2		6)(x						2			4)								dx .
					(x					6)(x									4)
								x		4
15.18.								x			1										dx .
15.18.			x		3	x					2										dx .
			x			x						x 1
15.20.			3x3 6x2 5x																					1
15.20.				(x 1)								2	(x		2					2)				dx .
				(x 1)									(x							2)

15.22.4 x3 3x2 8x dx .

x2 (x2 4)


15.24.	3x3		9x2 13x 27							dx .
15.24.	(x			2	16)(x 1)				2	dx .
	(x				16)(x 1)
15.26.	4x2 8x 6							dx .
15.26.	(x	2			3)(x	2	1)	dx .
	(x				3)(x		1)

15.28.49 2 4x22 147x dx .

x(x 49)

15.30. 3x3 2 2x2 29x 4 dx . (x 1)(x 7)

Задача 16

16.1.

3x2 x 28

dx .

4)(x

16.3.

16.5.

3x2 11x 8

dx .

2) x

16.7.

7x 20

dx .

2)(x

6x 14)

16.9.

2x x2 15

dx .

3)(x

2x 3)

16.11.

3x2 4x 9

dx .

(x 1)(x

2x 5)

16.13.

(2x2 10x 3)dx

(x 7)(x

4x 10)

16.15.

(3x2 4)dx

2)(x

16.17.

3x2 11x 16

dx .

(x 2) x

3x 4

16.2.

2x2 8x 13

dx .

1)(x

2x 4)

16.4.

dx .

16.6.

3x2 29

dx .

3)(x

4x 7)

16.8.

2x2 7x 9

dx .

4x 9)(x 3)

16.10.

16.12.

2x3 4x2 16x

dx .

(x 1)

16.14.x3 3 x 1 dx .


16.16.			(2x 3) dx							.
16.16.	x	2	(x		2	2x			2)	.
	x		(x			2x			2)
16.18.		(x3 x2 1)dx										; .
16.18.	(x		2	1)(x			2	x			1)	; .
	(x			1)(x				x			1)

3x2 13x 34 3x2 33

16.19.(x 2)(x2 4x 8)dx . 16.20. (x 5) x2 4x 9 dx .

16.21.		dx					.								16.22.			4x2 47							dx .
16.21.	8	x				3	.								16.22.	(x	4)(x			2		3x 9)			dx .
	8	x														(x	4)(x					3x 9)
16.23.	x5		2x3 4x 4										dx .		16.24.	(2x 5)dx						.
16.23.		x		4	2x				3	2x	2		dx .		16.24.	x	3	125				.
		x			2x					2x						x		125
16.25.				x2 28x 15										dx .	16.26.	x3	4x2 6x 13
																								dx .
								2
	(x				5)(x			2		5x		10)				x	4	6x	3		13x		2
	(x				5)(x					5x		10)				x		6x			13x

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