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Basic Integration Problems.pdf

Basic Integration Problems. I. Find the following integrals. 2. 1. (5 Evaluate the following definite integrals. 4. 2.



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Basic Integration Problems

I. Find the following integrals.

21. (5 8 5)x x dx

322. ( 6 9 4 3)x x x dx

3

23. ( 2 3)x x dx

238 5 64.dxxxx

15. ( )3x dxx

53

346. (12 9 )x x dx

2

247.xdxx

18.dxxx

29. (1 3 )t t dt

2210. (2 1)t dt

2311.y y dy

12.d

13. 7sin( )x dx

14. 5cos( )d

15. 9sin(3 )x dx

16. 12cos(4 )d

17. 7cos(5 )x dx

18. 4sin3

xdx

719. 4xe dx

420. 9

x e dx

21. 5cosx dx

622. 13te dt

II. Evaluate the following definite integrals.

42

11. (5 8 5)x x dx

3 29

12. ( 2 3)x x dx

9 4

13. ( )3x dxx

4 31

54.dxx

22

15. (1 3 )t t dt

122

26. (2 1)t dt

Solutions

I. Find the following integrals.

3

2251. (5 8 5) 4 53

xx x dx x x C 4

3 2 3 232. ( 6 9 4 3) 3 2 32

xx x x dx x x x C 3 2 5

2223. ( 2 3) 35

xx x dx x x C 23
23
12 2

8 5 6 84. 5 6

5 6 5 38 ( ) 8 ( )12

dx x x dxxxxx xxLn x Ln x Cxx 11 22
31
3122
22

115. ( )33

1 2 2

313 3 3

22
x dx x x dxx xxx x C 87
5334

3448 276. (12 9 )78

xxx x dx c 2 2

2447. 1 4xdx x dx x Cxx

3

2128.dx x dx Cx x x

34

2 2 339. (1 3 ) 334

ttt t dt t t dt C 53

2 2 4 24410. (2 1) 4 4 153

ttt dt t t dt t C 10

73233311.10

yy y dy y dy C 12.dC

13. 7sin( ) 7cos( )x dx x C

14. 5cos( ) 5sin( )dC

15. 9sin(3 ) 3cos(3 )x dx x C

16. 12cos(4 ) 3sin 4dC

7sin(5 )17. 7cos(5 )5

xx dx C

18. 4sin 12cos33

xxdx C 7

7419. 47

x xee dx C

4420. 9 36

xx e dx e C

5sin( )21. 5cosxx dx C

6

61322. 136

t tee dt C

II. Evaluate the following definite integrals.

43422
1 1

5 188 81. (5 8 5) 4 5 603 3 3

xx x dx x x 3 2 95
292
1 1

2 1026 22 10012. ( 2 3) 3 200.25 5 5 5

xx x dx x x 9319
22
44

1 2 2 20 403. ( ) 20 13.3333 3 3 33x dx x xx

44
3211

5 5 5 5 754. 2.34432 2 322dxxx

23422
1 1

3 44 5 575. (1 3 ) 14.253 4 3 12 4

ttt t dt

153122

2 2

4 4 7 254 876. (2 1) 17.45 3 15 15 5

ttt dt tquotesdbs_dbs21.pdfusesText_27
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