.

3.5 Integration of trigonometric functions

1.

(a) $${\frac{\sin^{4}{x}}{4} + C}$$ (b) $${\frac{1}{9}\sin^{3}{3x} + C}$$ (c) $${\frac{x}{2} + \frac{\sin{2x}}{4} + C}$$ (d) $${\sin{x} - \frac{\sin^{3}{x}}{3} + C}$$

(e) $${\frac{\cos^{7}{x}}{7} - \frac{\cos^{5}{x}}{5} + C}$$ (f) $${\frac{\cos{x}}{2} - \frac{\cos{5x}}{10} + C}$$ (g) $${\frac{\sin{x}}{2} - \frac{\sin{3x}}{6} + C}$$

(h) $${\frac{\sin{x}}{2} + \frac{\sin{3x}}{6} + C}$$ (i) $${\frac{\tan^{2}{x}}{2} + C}$$ (j) $${\frac{1}{2}(\sec{x}\tan{x} + \log\vert\sec{x} + \tan{x}\vert) + C}$$