　 $3$\displaystyle{\int f $ \sin x,\cos x $ dx }$

$3$\displaystyle{ f $ \sin x,\cos x $ }$ は $3$\displaystyle{ \sin x }$ と $3$\displaystyle{ \cos x }$
の関数のこと
$3$\displaystyle{\tan \frac{\hspace{2}x\hspace{2}}{\hspace{2}2\hspace{2}}=t}$ とおくと
$3$\displaystyle{ \sin x=\frac{\hspace{2} 2t \hspace{2}}{\hspace{2} 1+ {t}^{2} \hspace{2}} }$ ⇒
$3$\displaystyle{ \cos x=\frac{\hspace{2} 1- {t}^{2} \hspace{2}}{\hspace{2} 1+ {t}^{2} \hspace{2}} }$ ⇒
$3$\displaystyle{ dx=\frac{\hspace{2}2\hspace{2}}{\hspace{2} 1+ {t}^{2} \hspace{2}}dt }\hspace{5}}$ ⇒
したがって
$3$\displaystyle{f $ \sin x,\cos x $ dx=}$
$3$\displaystyle{\int f $ \frac{\hspace{2} 2t \hspace{2}}{\hspace{2} 1+{t}^{2} \hspace{2}},\frac{\hspace{2} 1- {t}^{2} \hspace{2}}{\hspace{2} 1+{t}^{2} \hspace{2}} $ \cdot \frac{\hspace{2}2\hspace{2}}{\hspace{2} 1+{t}^{2} \hspace{2}}dt}$