$3$\displaystyle{\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} { \cos }^{2}x \hspace{2}}dx }=\tan x+C}$

$3$\displaystyle{C}$ は積分定数

$3$\displaystyle{\tan x}$ の微分を参照のこと。

■応用公式
$3$\displaystyle{\begin{array}{lll}\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} { \cos }^{2} $ ax+b $ \hspace{2}}dx }& \vspace{6}\\ =\frac{\hspace{2}1\hspace{2}}{\hspace{2}a\hspace{2}}\tan $ ax+b $ +C& \vspace{6}\\ \end{array}}$
　 $3$\displaystyle{a}$ ， $3$\displaystyle{b}$ >は定数

■計算例
$3$\displaystyle{\begin{array}{lll}\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} { \cos }^{2} $ 3x+\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}4\hspace{2}} $ \hspace{2}}dx }& \vspace{6}\\ =\frac{\hspace{2}1\hspace{2}}{\hspace{2}3\hspace{2}}\tan $ 3x+\frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}4\hspace{2}} $ +C& \vspace{6}\\ \end{array}}$