3.5 三角関数の積分法

1.

(a) $${-\cos{x} + \frac{\cos^{3}{x}}{3}}$$(b) $${\frac{x}{2} - \frac{\sin{6x}}{12}}$$(c) $${\frac{\cos^{5}{x}}{5} - \frac{\cos^{3}{x}}{3}}$$

(d) $${\frac{1}{2}[\frac{-\cos{5x}}{5} + \cos{x}]}$$(e) $${-\cos{x} + \frac{2\cos^{3}{x}}{3} - \frac{\cos^{5}{x}}{5}}$$(f) $${\frac{1}{\pi}\tan{\pi x}}$$

(g) $${\log\vert\cos{x}\vert + \frac{1}{2}\sec^{2}{x}}$$(h) $${\frac{1}{3}\tan^{3}{x}}$$(i) $${\frac{\sec^{5}{x}}{5} - \frac{\sec^{3}{x}}{3}}$$

(j) $${\frac{1}{4}[\sec^{3}{x}\tan{x} + \frac{3}{2}(\sec{x}\tan{x} + \log\vert\sec{x} + \tan{x}\vert)}$$(k) $${\frac{2\sqrt{5}}{5}\tan^{-1}(\sqrt{5}\tan{\frac{x}{2}})}$$

(l) $${-x + \frac{4}{\sqrt{3}}\tan^{-1}{(\tan{(\frac{x}{2})} - \frac{1}{2})}}$$(m) $${\tan(\frac{x}{2}) + \log{\vert 1 + \tan^{2}{(\frac{x}{2})}\vert}}$$

(n) $${\frac{1}{4}\log{\vert\frac{\tan{x} - 1}{\tan{x} + 1}\vert} + \frac{x}{2}}$$ (o) $${\frac{1}{2}[x + \log{\vert\cos{x} + \sin{x}\vert}]}$$