please do 16, 34, 48, 66, 72, 79, 80, 82, 83
Exercises 6.1 Inspector Zoom Share Terms and Concepts 17. cos ( 3 - 6x) dx 1. Substitution "undoes" what derivative rule? 18 . sec ' ( 4 - x ) dx 2. T/F: One can use algebra to rewrite the integrand of an in- tegral to make it easier to evaluate. 19 . sec ( 2 x ) dx 35 . In (xox TIONS TO SELF X - X x2 4 4x + 9dx 80 *VX - 2dx In Exercises 53 - 78, evaluate the indefinite integral. Problems 20. tan? (x) sec? ( x ) dx sin (x) 36. xin (12 ) dx 53. / ( x3 + 3 ) 20 74. cos' ( x) + 1dx 81 . " sin xcos* dx In Exercises 3 -14, evaluate the indefinite integral to develop an understanding of Substitution. 21. *cos ( x ? ) dx In Exercises 37 - 42, use Substitution to evaluate the indefi- 54. / (3x7 + 2x) (5x3 + 5x7+ 2)" dx 75. ( x) dx nite integral involving rational functions. $2 ) / 2 x (1 - * 3 ) # dx 3. 3x2 (x) - 5) dx 22 . tan ? ( x ) dxa . ( x + 3 x + 1 dx cos (x ) dx x 55. / VI x x 76. 1-3 83. / ( * + 1 ) @ * + 2x + 3 dx 4 . / ( 2x - 5 ) ( * 2 - 5 * + 7 ) ' dx 23. cot x dx. Do not just refer to Theorem 6.1.2 for the an- 38 . (x + * + * + 1 dx 156. ( x ese ' ( x) + 1) dx 77. - 3x - 3 dx swer; justify it through Substitution. 84. [ 1 dx 5 . * ( 1 2 + 1 ) 8 dx 39. * - 1dx 57. sin ( x ) Vcos ( x ) dx x - 3 24 . cscx dx. Do not just refer to Theorem 6.1.2 for the an- 78. / Vx2 - 6x + 8 x swer; justify it through Substitution. 6. / (12x + 14 ) ( 3x 7 + 7x - 1) 5 dx 40. * + 2x - 5 dx 58 . sin ( 5 x + 1 ) dx 85. / x2 - 6x + 10 dx In Exercises 79 - 86, evaluate the definite integral. x - 3 In Exercises 25 - 32, use Substitution to evaluate the indefi- nite integral involving exponential functions. 59 . / x - 5 dx 79 5 dx 86. Val xz dx 7. / 2x + 7 dx 41. ( 3x - 5x+ dx x + 1 25. 3x-1 dx 60. 3x + 2 dx 42. * + 2x + 1 dy 8 .) / VZx + 3 dx *3 + 3x2 + 3xX 26 . ex - dx 61. ( 3x' + 4x7 + 2X - 22 dx In Exercises 43 - 52, use Substitution to evaluate the indefi- x2 + 3x + 5 9 . / V x + 3 dx nite integral involving inverse trigonometric functions. 62. 2x+7 27. ex- 2x + 1 ( x - 1 ) dx x2 + 7x + 3dx 43. / 2 + 7 8x 9(2x + 3) 10. -X dx V X 3. 3 x 2 + 9x + 7 x 28. [efax Vg - x z dx evx 64. X + 14x2 - 46x -dx 11. x2 - 7x + 1 Vx 29 . ex + 1 dx 45. / 75 - x2 dx 65. + 81 dx 12. = dx VXS + 1 30 . e - e e 2x 46 . XV x 2 _ 9 dx 66 .) / AX2 + 1 dx 13 . it * 2 3 3x dx 47. / VX - 16*2 dx 67. XVAX? _ Idx 14. In(x) dx 32 . 1 4 2X dx 48 . VI - x dx 68. 16 - 9X2 dx In Exercises 15 - 24, use Substitution to evaluate the indefi- In Exercises 33 - 36, use Substitution to evaluate the indefi- 1 49. x 2 - 2x + 8 dx 69. - 3X - 2 nite integral involving trigonometric functions. x2 - 2x + 10 dx nite integral involving logarithmic functions. 2 70. 7-2x 15 . sin? (x ) cos ( x ) dx 33 . In* dx 50 . V - x 2 + 6 * + 7 x2+ 12x+ 61 71. * + 5x - 2 16. cos ( x ) sin ( x ) dx 34 ( In x ) 2 51. x2 - 10x + 32 dx 5 72 . x 52 . * 2 + 6 * + 34 X x2 + 9
