不定積分の公式集 (deuterium)

三角関数：その他いろいろ	不定積分
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三角関数
　・その他

tan関係

$\int {\color{Red} \frac{\tan ax}{1 \pm \tan ax} } \, dx = - \frac{p}{a(p^2+1)} \ln \left ( p \cos ax \pm \sin ax \right ) \pm \frac{x}{p^2+1}+ C$

$\int {\color{Red} \frac{\csc^2 ax}{\cot ax} } \, dx = - \frac{1}{a} \ln \left ( \cot ax \right ) + C$

$\int {\color{Red} \tan^n ax \, \sec^2 ax } \, dx = \int {\color{Red} \frac{\tan^n ax}{\cos^2 ax} } \, dx = \frac{\tan^{n+1} ax}{(n+1)a} + C$

$\int {\color{Red} \sec^n ax \, \tan ax } \, dx = \frac{\sec^n ax}{na} + C$

$\int {\color{Red} \cot^n ax \csc^2 ax } \, dx = - \frac{ \cot^{n+1} ax}{(n+1)a} + C$

$\int {\color{Red} \frac{\sec^2 ax}{\tan ax} } \, dx = \int {\color{Red} \frac{1}{\cos^2 ax \, \tan ax} } \, dx = \frac{1}{a} \ln \left ( \tan ax \right ) + C$