## Answers to ExercisesforSection 4: Integrals of Trigonometric Functions

1. $-(\cos x + \sin x) + C$

3. $-(1/2)\ln \|\cosec(2x-3) + \cotan(2x-3)\| + C$

5. $(1/2)\ln \|\sin(x^2-1)\| + C$

7. $(\sin^4x)/4 + C$

9. $-(1/2)\cotan(2x-3) + C$

11. $\cos(1/x) + C$

13. $-(1-\sin x)^2/2 + C$

15. $-\ln \|\cos(e^x)\| + C$

17. $-(2x-1)\cos x + 2\sin x + C$

19. $2x^3\sin(x/2) + 12x^2\cos(x/2) - 48x\ \sin(x/2) - 96\cos(x/2) + C$

21. $e^{-x}(\sin x - \cos x)/2 + C$

23. $(\sin x)(\ln \|\sin x\|) - \sin x + C$

29. $2$

31. $(\ln\ 2)/2$