Answer Happy

Evaluate the following integrals using integration byparts.
Q- 21 AND 25 AND 27
Getting Started 19. ∫x10lnx​dx 20. ∫sin−1xdx 1. On which derivative rule is integration by parts based? 21. ∫xsinxcosxdx 22. ∫e2xsinexdx 2. Use integration by parts to evaluate ∫xcosxdx with u=x and dv=cosxdx 3. Use integration by parts to evaluate ∫xlnxdx with u=lnx and 23. ∫x2sin2xdx 24. ∫x2e4xdx dv=xdx. 4. How is integration by parts used to evaluate a definite integral? 25. ∫t2e−tdt 26. ∫t3sintdt 5. What type of integrand is a good candidate for integration by 27. ∫excosxdx 28. ∫e3xcos2xdx 6. How would you choose dv when evaluating ∫xneμudx using 29. ∫e−xsin4xdx 30. ∫e−2θsin6θdθ integration by parts? 7-8. Use a substitution to reduce the following integrals to ∫lnudu. 31. ∫e3xsinexdx 32. ∫01​x22xdx Then evaluate the resulting integral using the formula for ∫lnxdx. 33. ∫0π​xsinxdx 34. ∫1e​ln2xdx 7. ∫(sec2x)ln(tanx+2)dx 8. ∫(cosx)ln(sinx)dx 35. ∫0π/2​xcos2xdx 36. ∫0ln2​xexdx Practice Exercises 37. ∫1e2​x2lnxdx 38. ∫x2ln2xdx 9-40. Integration by parts Evaluate the following integrals using integratien by parts: 39. ∫01​sin−1ydy 40. ∫ex​dx 9. ∫xcos5xdx 10. ∫xsin2xdx 41. Evaluate the integral in part (a) and then use this result to evaluate 11. ∫tc6tdt 12. ∫2xc3xdx the integral in part (b).