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11.60: A.9.4- Section 9.4 Answers

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Dec 31, 2022
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- 11.59: A.9.3 Section 9.3 Answers
- 11.61: A Brief Table of Integrals (by Trench)

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1. $y_{p}=2x^{3}$

2. $y_{p}=\frac{8}{105}x^{7/2}e^{-x^{2}}$

3. $y_{p}=x\ln |x|$

4. $y_{p}=-\frac{2(x^{2}+2)}{x}$

5. $y_{p}=-\frac{xe^{-3x}}{64}$

6. $y_{p}=-\frac{2x^{2}}{3}$

7. $y_{p}=-\frac{e^{-x}(x+1)}{x}$

8. $y_{p}=2x^{2}\ln |x|$

9. $y_{p}=x^{2}+1$

10. $y_{p}=\frac{2x^{2}+6}{3}$

11. $y_{p}=\frac{x^{2}\ln |x|}{3}$

12. $y_{p}=-x^{2}-2$

13. $\frac{1}{4}x^{3}\ln |x|-\frac{25}{48}x^{3}$

14. $y_{p}=\frac{x^{5/2}}{4}$

15. $y_{p}=\frac{x(12-x^{2})}{6}$

16. $y_{p}=\frac{x^{4}\ln |x|}{6}$

17. $y_{p}=\frac{x^{3}e^{x}}{2}$

18. $y_{p}=x^{2}\ln |x|$

19. $y_{p}=\frac{xe^{x}}{2}$

20. $y_{p}=\frac{3xe^{x}}{2}$

21. $y_{p}=-x^{3}$

22. $y=-x(\ln x)^{2}+3x+x^{3}-2x\ln x$

23. $y=\frac{x^{3}}{2}(\ln |x|)^{2}+x^{2}-x^{3}+2x^{3}\ln |x|$

24. $y=-\frac{1}{2}(3x+1)xe^{x}-3e^{x}-e^{2x}+4xe^{-x}$

25. $y=\frac{3}{2}x^{4}(\ln x)^{2}+3x-x^{4}+2x^{4}\ln x$

26. $y=-\frac{x^{4}+12}{6}+3x-x^{2}+2e^{x}$

27. $y=\left(\frac{x^{2}}{3}-\frac{x}{2}\right)\ln |x|+4x-2x^{2}$

28. $y=-\frac{xe^{x}(1+3x)}{2}+\frac{x+1}{2}-\frac{e^{x}}{4}+\frac{e^{3x}}{2}$

29. $y=-8x+2x^{2}-2x^{3}+2e^{x}-e^{-x}$

30. $y=3x^{2}\ln x-7x^{2}$

31. $y=\frac{3(4x^{2}+9)}{2}+\frac{x}{2}-\frac{e^{x}}{2}+\frac{e^{-x}}{2}+\frac{e^{2x}}{4}$

32. $y=x\ln x+x-\sqrt{x}+\frac{1}{x}+\frac{1}{\sqrt{x}}$

33. $y=x^{3}\ln |x|+x-2x^{3}+\frac{1}{x}-\frac{1}{x^{2}}$

35. $y_{p}=\int_{x_{0}}^{x}\frac{e^{(x-t)}-3e^{-(x-t)}+2e^{-2(x-t)} }{6}F(t)dt$

36. $y_{p}=\int_{x_{0}}^{x}\frac{(x-t)^{2}(2x+t)}{6xt^{3}}F(t)dt$

37. $y_{p}=\int_{x_{0}}^{x}\frac{xe^{(x-t)}-x^{2}+x(t-1) }{t^{4}}F(t)dt$

38. $y_{p}=\int_{x_{0}}^{x}\frac{x^{2}-t(t-2)-2te^{(x-t)}}{2x(t-1)^{2}}F(t)dt$

39. $y_{p}=\int_{x_{0}}^{x}\frac{e^{2(x-t)}-2e^{(x-t)}+2e^{-(x-t)}-e^{-2(x-t)}}{12}F(t)dt$

40. $y_{p}=\int_{x_{0}}^{x}\frac{(x-t)^{3}}{6x}F(t)dt$

41. $y_{p}=\int_{x_{0}}^{x}\frac{(x+t)(x-t)^{3}}{12x^{2}t^{3}}F(t)dt$

42. $y_{p}=\int_{x_{0}}^{x}\frac{e^{2(x-t)}(1+2x)+e^{-2(x-t)}(1-2t)-4x^{2}+4t^{2}-2}{32t^{2}}F(t)dt$

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