置換積分の応用：f'(x)/f(x)の積分

\Large\int\frac{f^{\prime}(x)}{f(x)}dx=\log|f(x)|+C

計算例

\large\int\tan xdx=\int\frac{\sin x}{\cos x}dx=\int\frac{-(\cos x)^{\prime}}{\cos x}dx=-\log|\cos x|+C