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SalasSV_08_04_ex

# SalasSV_08_04_ex - 472 CHAPTER 8 TECHNIQUES OF INTEGRATION...

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472 CHAPTER 8 TECHNIQUES OF INTEGRATION EXERCISES 8.4 Calculate the integral. 1. dx a 2 x 2 . 2. 4 5 / 2 x x 2 4 dx . 3. x 2 1 dx . 4. x 4 x 2 dx . 5. x 2 4 x 2 dx 6. x 2 x 2 4 dx . 7. x (1 x 2 ) 3 / 2 dx . 8. x 2 4 + x 2 dx . 9. 1 / 2 0 x 2 (1 x 2 ) 3 / 2 dx . 10. x a 2 + x 2 dx . 11. x 4 x 2 dx . 12. 2 0 x 3 16 x 2 dx . 13. 5 0 x 2 25 x 2 dx . 14. 1 x 2 x 4 dx . 15. x 2 ( x 2 + 8) 3 / 2 dx . 16. a 0 a 2 x 2 dx . 17. dx x a 2 x 2 . 18. x 2 1 x dx . 19. 3 0 x 3 9 + x 2 dx . 20. dx x 2 a 2 x 2 . 21. dx x 2 a 2 + x 2 . 22. dx ( x 2 + 2) 3 / 2 . 23. 1 0 dx (5 x 2 ) 3 / 2 . 24. dx e x 4 + e 2 x . 25. dx x 2 x 2 a 2 . 26. e x 9 e 2 x dx . 27. dx e x e 2 x 9 . 28. dx x 2 2 x 3 . 29. dx ( x 2 4 x + 4) 3 / 2 . 30. x 6 x x 2 dx . 31. x 6 x x 2 8 dx . 32. x + 2 x 2 + 4 x + 13 dx . 33. x ( x 2 + 2 x + 5) 2 dx . 34. x x 2 2 x + 3 dx . 35. Verify the integration formula (8.2.7): sec 1 x dx = x sec 1 x ln x + x 2 1 + C . 36. Calculate a 2 x 2 x dx by using: (a) The substitution u = a 2 x 2 .

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SalasSV_08_04_ex - 472 CHAPTER 8 TECHNIQUES OF INTEGRATION...

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