# 4.8 - 4.8Antiderivatives Exercises 4.8 Finding...

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Chapter 5 / Exercise 10
Intermediate Algebra
Tussy/Gustafson
Expert Verified
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
Expert Verified
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