integration_review

integration_review - 41. Z 1 e x + 1 dx [Hint: Try...

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Integration Study Sheet: This is a collection of integration problems. To solve these problems, you will need to use substitution, integration by parts, the method of partial fractions, and trigonometric substitution. 1. Z (2 x + 5)( x 2 + 5 x ) 7 dx 2. Z (3 - x ) 10 dx 3. Z 7 x + 9 dx 4. Z x 3 (1 + x 4 ) 1 / 3 dx 5. Z e 5 x +2 dx 6. Z sin(ln x ) x dx 7. Z x + 2 x 2 + 4 x - 3 dx 8. Z ± 3 x 2 +1 ² ± x ² dx 9. Z 1 x ln x dx 10. Z cos(5 x ) e sin(5 x ) dx 11. Z π 0 x sin( x 2 ) dx 12. Z x 4 - x dx [Hint: If u = 4 - x , what does that make x in terms of u ?] 13. Z xe x dx 14. Z x sin xdx 15. Z x ln xdx 16. Z ln xdx 17. Z ln x x 5 dx 18. Z x 2 e 3 x dx 19. Z x 3 ln(5 x ) dx 20. Z x x + 3 dx
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Integration Study Sheet 21. Z sin 2 ( x ) dx 22. Z x sin( x ) cos( x ) dx 23. Z x cos( x ) dx 24. Z x 2 cos( x ) dx 25. Z e x cos( x ) dx [Hint: Do integration by parts twice.] 26. Z 1 x 2 - 4 dx 27. Z x x 2 - 4 dx 28. Z 1 x ( x + 1) dx 29. Z 1 x 2 ( x + 1) dx 30. Z x - 1 x 2 - 16 dx 31. x + 7 x 2 ( x + 2) dx 32. 1 x ( x 2 + 1) 33. Z 1 1 - x 2 dx 34. Z 1 1 - 4 x 2 dx 35. Z 2 1 x 2 - 1 x dx 36. Z 4 0 x 2 4 - x 2 dx 37. Z 1 x 9 - x 2 dx 38. Z x 5 x 2 + 25 dx 39. Z 1 x 2 + 4 x + 5 dx 40. Z x 2 1 + x 2 dx
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Integration Study Sheet
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Unformatted text preview: 41. Z 1 e x + 1 dx [Hint: Try multiplying by e x e x .] 42. Z e x dx 43. Z 1 + e x dx 44. Z (1 + x ) 9 dx 45. Z x 1 + x 3 dx 46. Z 1 x + x x dx 47. Z 1 x + 1 + x dx 48. Z x sin 2 ( x ) cos( x ) dx 49. Z x sin 2 ( x ) dx 50. Z x tan 2 ( x ) dx 51. Z ln( x + 1) x 2 dx 52. Z xe x 1 + e x dx 53. Z 1 1 x dx 54. Z 3 1 ( x-2) 2 dx 55. Z e ln x x dx 56. Z e 1 x (ln x ) 2 dx 57. Z xe-x dx 58. Z xe-x 2 dx 59. Z 1 arctan x x 2 + 1 dx 60. Z f ( x ) dx, where f ( x ) = ( 1 x if x 1 1 x 2 if x 1...
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This note was uploaded on 11/29/2010 for the course MATH 1700 taught by Professor Staff during the Spring '08 term at Missouri (Mizzou).

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integration_review - 41. Z 1 e x + 1 dx [Hint: Try...

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