Practice Exercises

A1. ∫(3x² – 2x + 3) dx =

(A) x³ – x² + C
(B) 3x³ – x² + 3x + C
(C) x³ – x² + 3x + C
(D) 

A2. 

A3. 

A4. ∫(2 – 3x)⁵dx =

A5. 

A6. 

A7. 

A8. 

A9. ∫ cos 3x dx=

(A) 3 sin 3x + C
(B) –sin 3x + C
(C) 
(D) 

A10. 

A11. 

A12. 

A13. 

A14. 

A15. 

A16. 

(A) 
(B) x + 2 ln |x| + C
(C) x + ln |2x| + C
(D) 

A17. 

A18. 

A19. 

(A) 3x^4/3 – 2x^5/2 – 2x^1/2 + C
(B) 3x^4/3 – 2x^5/2 + 2x^1/2 + C
(C) 
(D) 

A20. 

A21. 

A22. 

A23. ∫ sin²θ cosθ dθ =

A24. 

A25. ∫ t cos(4t²)dt =

CHALLENGE A26. ∫ cos² 2x dx =

A27. ∫ sin 2θ dθ =

(A) 
(B) –2 cos 2θ + C
(C) cos²θ + C
(D)

*A28. ∫ x cos x dx =

(A) x sin x + C
(B) x sin x + cos x + C
(C) x sin x – cos x + C
(D) cos x – x sin x + C

A29. 

A30. 

A31. 

(A) 2 ln sin |θ – 1| + C
(B) –csc(θ – 1) + C
(C) –cot(θ – 1) + C
(D) csc(θ – 1) + C

CHALLENGE A32. 

A33. ∫ sec^3/2x tan x dx =

A34. ∫tan θ dθ =

(A) –ln |cos θ| + C
(B) sec²θ + C
(C) ln |sin θ| + C
(D) –ln |sec θ| + C

A35. 

(A) 
(B) 
(C) –cot x + C
(D) –csc 2x + C

A36. 

(A) (tan^–1y)² + C
(B) ln (1 + y²) + C
(C) ln (tan^–1y) + C
(D) 

A37. ∫ 2 sin θ cos²θ dθ =
(A) 
(B) 
(C) sin²θ cos θ + C
(D) cos³θ + C

A38. 

A39. ∫ cot 2u du =

(A) ln |sin u| + C
(B) 
(C) 
(D) 2 ln |sin 2u| + C

A40. 

(A) x + ln |e^x – 1| + C
(B) x – e^x + C
(C) 
(D) ln |e^x – 1| + C

*A41. 

A42. 

A43. ∫ cos θ e^{sin θ}dθ =

(A) e^{sin θ + 1} + C
(B) e^{sin θ} + C
(C) –e^{sin θ} + C
(D) e^{cos θ} + C

A44. ∫ e^2θ sin e^2θdθ =

(A) cos e^2θ + C
(B) 2e^4θ (cos e^2θ + sin e^2θ) + C
(C) 
(D) –2 cos e^2θ+ C

A45. 

*A46. ∫ xe^–x dx =

(A) e^–x (1 – x) + C
(B) 
(C) –e^–x(x + 1) + C
(D) e^–x (x + 1) + C

*A47. ∫ x²e^x dx =

(A) e^x(x² + 2x) + C
(B) e^x(x² – 2x – 2) + C
(C) e^x (x² – 2x + 2) + C
(D) e^x(x – 1)² + C

A48. 

(A) x – ln |e^x – e^–x| + C
(B) x + 2 ln |e^x – e^–x| + C
(C) ln |e^x – e^–x| + C
(D) ln (e^x + e^–x) + C

A49. 

(A) tan^–1e^x + C
(B) 
(C) ln (1 + e^2x) + C
(D) 

A50. 

A51. 

*A52. ∫ x³ ln x dx 

*A53. ∫ ln η dη =
(A) 
(B) η (ln η – 1) + C
(C) 
(D) η ln η + η + C

*A54. ∫ ln x³dx =

(A) 
(B) 3x (ln x – 1) + C
(C) 3 ln x (x – 1) + C
(D) 

*A55. 

A56. 

A57. 

(A) y – 2 ln |y + 1| + C
(B) 
(C) 
(D) 1 – 2 ln |y + 1| + C

A58. 

(A) ln(x² + 2x + 2) + C
(B) ln |x + 1| + C
(C) arctan(x + 1) + C
(D) 

A59. 

*A60. ∫ e^θ cos θ dθ =

(A) e^θ(cos θ – sin θ) + C
(B) 
(C) 2e^θ(sin θ + cos θ) + C
(D) 

A61. 

*A62. ∫ u sec²u du =

(A) u tan u + ln |cos u| + C
(B) 
(C) 
(D) u tan u – ln |sin u| + C

CHALLENGE A63. 

CHALLENGE A64. 

CHALLENGE A65. 

CHALLENGE A66. 

(A) tan^–1e^x + C
(B) e^x– ln (1 + e^x) + C
(C) e^x – x + ln |1 + e^x| + C
(D) 

A67. 

(A) sec θ tan θ + C
(B) ln (1 + sin²θ) + C
(C) tan^–1 (sin θ) + C
(D) 

*A68. ∫ arctan x dx =

(A) x arctan x – ln (1 + x²) + C
(B) x arctan x + ln (1 + x²) + C
(C) 
(D) 

CHALLENGE A69. 

(A) –ln |1 – e^x| + C
(B) x – ln |l – e^x| + C
(C) 
(D) e^–x ln |l + e^x| + C

A70. 

A71. ∫ e^{2 ln u}du =

A72. 

CHALLENGE A73. ∫ (tan θ – 1)²dθ =

(A) sec θ + θ + 2 ln |cos θ| + C
(B) tan θ + 2 ln |cos θ| + C
(C) tan θ – 2 sec²θ + C
(D) tan θ – 2 ln |cos θ| + C

CHALLENGE A74. 

(A) sec θ – tan θ + C
(B) ln (1 + sin θ) + C
(C) ln |sec θ + tan θ| + C
(D) tan θ – sec θ + C

A75. A particle starting at rest at t = 0 moves along a line so that its acceleration at time t is 12t ft/sec². How much distance does the particle cover during the first 3 seconds?

(A) 32 feet
(B) 48 feet
(C) 54 feet
(D) 108 feet

A76. The equation of the curve whose slope at point (x,y) is x² – 2 and which contains the point (1,–3) is

A77. A particle moves along a line with acceleration 2 + 6t at time t. When t = 0, its velocity equals 3 and it is at position s = 2. When t = 1, it is at position s =

(A) 5
(B) 6
(C) 7
(D) 8

A78. Find the acceleration (in ft/sec²) needed to bring a particle moving with a velocity of 75 ft/sec to a stop in 5 seconds.

(A) –3
(B) –6
(C) –15
(D) –25

*A79.