= Theorem =
> $\int\tan x dx=-\ln|\cos x|+C=\ln|\sec x|+C$

= Proof =
$\int\tan x dx$
$=\int\frac{\sin x}{\cos x}dx$
 치환:
 $u=\cos x$
 $du=-\sin x dx$
 $\sin x dx=-du$
$=\int\frac1u(-du)$
$=-\int\frac1udu$
$=-\ln|u|+C$
$=-\ln|\cos x|+C$
$=\ln|\sec x|+C$

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