原始関数の一覧
∫ ln  x d x = x ln  x − x + C {\displaystyle \int \ln x\,dx=x\ln x-x+C}
∫ log α  x d x = 1 ln  α ( x ln  x − x ) + C {\displaystyle \int \log _{\alpha }x\,dx={\frac {1}{\ln \alpha }}\left({x\ln x-x}\right)+C}
∫ x n ln  x d x = x n + 1 ( n + 1 ) 2 [ ( n + 1 ) ln  x − 1 ] + C {\displaystyle \int x^{n}\ln x\,dx={\frac {x^{n+1}}{(n+1)^{2}}}[(n+1)\ln x-1]+C}
∫ 1 x ln  x d x = ln  ( ln  x ) + C {\displaystyle \int {\frac {1}{x\ln {x}}}\,dx=\ln {(\ln {x})}+C}
∫ 1 x ( a x + b ) d x = − 1 b ln  | a x + b x | + C {\displaystyle \int {\frac {1}{x(ax+b)}}\,dx=-{\frac {1}{b}}\ln \left|{\frac {ax+b}{x}}\right|+C}
∫ 1 x 2 ( a x + b ) d x = a b 2 ln  | a x + b x | − 1 b x + C {\displaystyle \int {\frac {1}{x^{2}(ax+b)}}\,dx={\frac {a}{b^{2}}}\ln \left|{\frac {ax+b}{x}}\right|-{\frac {1}{bx}}+C}