対数関数の原始関数の一覧
∫ e x ( x ln  x − x − 1 x ) d x = e x ( x ln  x − x − ln  x ) {\displaystyle \int e^{x}\left(x\ln x-x-{\frac {1}{x}}\right)\;dx=e^{x}(x\ln x-x-\ln x)}
∫ 1 e x ( 1 x − ln  x ) d x = ln  x e x {\displaystyle \int {\frac {1}{e^{x}}}\left({\frac {1}{x}}-\ln x\right)\;dx={\frac {\ln x}{e^{x}}}}
∫ e x ( 1 ln  x − 1 x ln 2  x ) d x = e x ln  x {\displaystyle \int e^{x}\left({\frac {1}{\ln x}}-{\frac {1}{x\ln ^{2}x}}\right)\;dx={\frac {e^{x}}{\ln x}}}