10B_integrals.pdf - 102 Integration Problems c 2018 Adam...

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102 Integration Problems c 2018 Adam Bowers The following questions are intended to provide practice for evaluating indefinite integrals. To solve these problems, you will need to use substitution, integration by parts, the method of partial fractions, and trigonometric substitution. The last section contains some improper integrals. Please be aware that not all of these problems are of equal difficulty level. Some of the problems can be quite challenging. Indeed, some of the integrals in the “Challenge Integrals” section can be very difficult. Integrals 1. Z (2 x + 5)( x 2 + 5 x ) 7 dx 2. Z e 5 x +2 dx 3. Z xe x dx 4. Z 1 x ( x + 1) dx 5. Z 1 1 - 4 x 2 dx 6. Z (3 - x ) 10 dx 7. Z 7 x + 9 dx 8. Z 1 0 ( x + 1) e 2 x dx 9. Z 2 1 x 2 - 1 x dx 10. Z 1 x 2 ( x + 1) dx 11. Z x - 1 x 2 - 16 dx 12. Z x 3 (1 + x 4 ) 1 / 3 dx 13. Z 4 x cos(3 x 2 ) dx 14. Z sin(ln( x )) x dx 15. Z 3 x dx 16. Z 3 ( x 2 +1) · x dx 1
17. Z 1 x ln( x ) dx 18. Z cos(5 x ) e sin(5 x ) dx 19. Z π 0 x sin( x 2 ) dx 20.

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