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sampletest_1

# sampletest_1 - 2sin √ x C 9 2 √ x sin √ x cos √ x C...

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1. Z x dx 4 + 9 x 4 2. Z x 3 dx 4 + x 4 3. Z e 4 x dx 9 - e 8 x 4. Z xe 5 x 2 dx 5. Z e 4 x dx 9 - e 4 x 6. Z x 3 x 2 dx 7. Z e x x dx = Z e x 1 x dx 8. Z cos x x dx 9. Z cos x dx 10. Z e x dx 11. Z dx 2 - 3 x 12. Z ln x x dx = Z (ln x ) 1 x dx 13. Z e 3 x e 3 x + 5 ln( e 3 x + 5) dx 14. Z ln x dx 15. Z Arcsin x dx 16. Z x Arctan x dx 17. Z e cos 3 x sin 3 x dx 18. Z 5 cos 3 x sin 3 x dx 19. Z x 5 ln x dx 20. Z sin 2 5 x dx 21. Z cos 4 3 x dx 22. Z sin 4 x cos 5 x dx 23. Z tan 4 x sec 4 x dx 24. Z tan 3 x sec 3 x dx 25. Z dx x (1 + x ) In 26–27, use a trigonometric substitu- tion. 26. Z du u 2 - a 2 27. Z a 2 - u 2 du 28. Z 3 x + 4 8 + 2 x - x 2 dx 29. Z 3 x + 4 x 2 - 6 x + 13 dx

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30. Z x 3 e x 2 dx = Z ( x 2 )[ e x 2 x dx ] = Z ( u )[ dv ] 31. Z x 3 cos x 2 dx = Z ( x 2 )[cos x 2 x dx ] = Z ( u )[ dv ] 32. Z x 3 dx 3 5 + x 2 = Z ( x 2 )[(5 + x 2 ) - 1 3 x dx ] = Z ( u )[ dv ] 33. Find the partial fraction decompo- sition. Be sure to find A.B.C, etc. There is nothing to be integrated. (a) 3 x ( x - 1)( x + 2) 2 (b) x ( x - 1)( x 2 - 2 x + 2) 34. Integrate by parts twice. Use cir- cular integration to show (a) Z e ax cos bx dx = e ax a 2 + b 2 ( a cos bx + b sin bx )+ C (b) Z e ax sin bx dx = e ax a 2 + b 2 ( a sin bx - b cos bx )+ C Answers 1. 1 12 Arctan 3 x 2 2 + C 2. 1 4 ln(4 + x 4 ) + C 3. 1 4 Arcsin e 4 x 3 + C 4. 1 10 e 5 x 2 + C 5. - 1 2 9 - e 4 x +
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Unformatted text preview: 2sin √ x + C 9. 2( √ x sin √ x + cos √ x ) + C 10. 2( √ x-1) e √ x + C 11.-2 3 √ 2-3 x + C 12. 1 2 (ln x ) 2 + C 13. 1 6 [ln( e 3 x + 5)] 2 + C 14. x ln x-x + C 15. x Arcsin x + √ 1-x 2 + C 16. 1 2 ( x 2 Arctan x-x + Arctan x )+ C 17.-1 3 e cos3 x + C 18.-1 3ln5 5 cos3 x + C 19. x 6 6 ± ln x-1 6 ² + C 20. x 2-1 20 sin10 x + C 21. 1 4 ± 3 2 x + 1 3 sin6 x + 1 24 sin12 x ² + C 22. 1 5 sin 5 x-2 7 sin 7 x + 1 9 sin 9 x + C 23. 1 5 tan 5 x + 1 7 tan 7 x + C 24. 1 5 sec 5 x-1 3 sec 3 x + C 25. 2 Arctan √ x + C...
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