4.8 - 4.8Antiderivatives Exercises 4.8 Finding...

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Intermediate Algebra
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Chapter 5 / Exercise 10
Intermediate Algebra
Tussy/Gustafson
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4.8  Antiderivatives 287Finding AntiderivativesIn Exercises 1–24, find an antiderivative for each function. Do as many as you can mentally. Check your answers by differentiation.1. a. 2xb. x2c. x2-2x+1 2. a. 6x b. x7c. x7-6x+83. a. -3x-4b. x-4c. x-4+2x+3 4. a. 2x-3 5. a. 1x2b. 5x2c. 2-5x2 6. a. -2x3 7. a. 322xb. 122xc. 2x+12x 8. a. 4323x 23x9. a. 23x-1>3b. 13x-2>3c. -13x-4>3 10. a. 12x-1>2 b. -12x-3>2c. -32x-5>211. a. 1xb. 7xc. 1-5x 12. a. 13x 13. a. -psin pxb. 3 sin xc. sin px-3 sin 3x 14. a. pcos px 15. a. sec2xb. 23sec2x3c. -sec23x2 16. a. csc2x 17. a. csc xcot xb. -csc 5xcot 5xc. -pcsc px2cot px2 18. a. sec xtan x b. 4 sec 3xtan 3xc. sec px2tan px219. a. e3xb. e-xc. ex>2 20. a. e-2x 21. a. 3xb. 2-xc. a53bx 22. a. x23 23. a. 221-x2b. 12(x2+1)c. 11+4x2 24. a. x-a12bx Finding Indefinite IntegralsIn Exercises 25–70, find the most general antiderivative or indefinite integral. You may need to try a solution and then adjust your guess. Check your answers by differentiation.25. L(x+1) dx26. L(5-6x) dx27. La3t2+t2bdt28. Lat22+4t3bdt29. L(2x3-5x+7) dx30. L(1-x2-3x5) dx31. La1x2-x2-13bdx32. La15-2x3+2xbdx33. Lx-1>3dx34. Lx-5>4dx35. L12x+23x2dx36. La2x2+22xbdx37. La8y-2y1>4bdy38. La17-1y5>4bdy39. L2x(1-x-3) dx40. Lx-3(x+1) dx41. Lt2t+2tt2dt42. L4+2tt3dt43. L(-2 cos t) dt44. L(-5 sin t) dt45. L7 sin u3du46. L3 cos 5udu47. L(-3 csc2x) dx48. La-sec2x3bdx49. Lcsc ucot u2du50. L25sec utan udu51. L(e3x+5e-x) dx52. L(2ex-3e-2x) dx53. L(e-x+4x)dx54. L(1.3)xdx55. L(4 sec xtan x-2 sec2x) dx56. L12(csc2x-csc xcot x) dx57. L(sin 2x-csc2x) dx58. L(2 cos 2x-3 sin 3x) dx59. L1+cos 4t2dt60. L1-cos 6t2dt61. La1x-5x2+1bdx62. La221-y2-1y1>4bdy63. L3x23 dx 64. L x 2 2 - 1 dx Exercises 4.8
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Chapter 5 / Exercise 10
Intermediate Algebra
Tussy/Gustafson
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288Chapter 4:Applications of Derivatives 84. Right, or wrong? Say which for each formula and give a brief reason for each answer. a. b. c. Ltan usec2udu=sec3u3+CLtan usec2udu=12tan2u+C

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