integrals - Calculus 1 grals Practice Antiderivatives and...

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Unformatted text preview: Calculus 1 grals Practice Antiderivatives and Inte- 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. x cos(x2 ) − √ tan3 sec2 tdt x 1/ 3 dx 2 + x 4/3 π /2 0 2 dx 1 − x2 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. (2x + sec2 (2x)) dx √ 1 x2 1 − x3 dx −2 1/2 arctan(2x) dx 1 + 4x2 e 1 cos x dx 1 + sin2 x 2 (x2 sin(x3 ) + xe−x ) dx cos θ dθ sin3 θ −2x + 1 dx 1 − x2 + x et √ dt 1 − e2t x 1 √ dx 0 3 + 2x2 ln x + cot x dx x cos t sin3 t dt x−2 e1/x dx x 1 + (ln x)2 dx 3 )2/3 (1 + x x √ 1 + ln x arctan x + dx x 1 + x2 arcsin x √ + (x − 1)1/2 dx 1 − x2 ex x √ + dx 1 − x4 1 + e2x π 0 2 (2 + ln x) 1/3 dx x (3x − sin2 x cos x) dx 1 dx (use x = 3 sin θ) (9 − x2 )3/2 x1/2 cos(x3/2 ) dx 1 dx (use x = 2 sin θ) (4 − x2 )1/2 12 x sec2 (x3 ) dx 0 √ 9 − x2 dx (use x = 3 sin θ) x 1/5 √ dx 1 + 2x6/5 ex dx (note: same as 1 + ex (3x ex + (cos x)esin x ) dx ex √ + e−3/2 dx x 5 3 √ 1 e−x + 1 dx) e 1 cos x(1 + sin x)2 dx (1 + ln x)−2 + tan x dx x x(2 − 5x2 )2/5 dx π /6 0 √ cos x dx 1 − sin x (x + 2)2 dx hint: Long divide x−2 2t + 3 dt hint: Long divide 3t + 2 1 (x − 1)3 + dx (5 − 2x)2 x2 1 sec2 x + dx x ln x tan x x + e2x + (2x + 1)10 dx 2 + e2x x dx 5 (use x = tan θ) 2 25 + 16x 4 See also text exercises on pages 420 - 421. Check your answers on Maple! 1 ...
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