対数関数の原始関数の一覧
{\displaystyle \int {\frac {dx}{\ln x}}=\ln |\ln x|+\ln x+\sum _{k=2}^{\infty }{\frac {(\ln x)^{k}}{k\cdot k!}}}
∫ d x ( ln  x ) n = − x ( n − 1 ) ( ln  x ) n − 1 + 1 n − 1 ∫ d x ( ln  x ) n − 1 (for n ≠ 1 ) {\displaystyle \int {\frac {dx}{(\ln x)^{n}}}=-{\frac {x}{(n-1)(\ln x)^{n-1}}}+{\frac {1}{n-1}}\int {\frac {dx}{(\ln x)^{n-1}}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}
∫ ( ln  x ) x d x = ( ln  x ) x − 1 + ( ln  ( ln  x ) ) ( ln  x ) x {\displaystyle \int (\ln x)^{x}\;dx=(\ln x)^{x-1}+\left(\ln(\ln x)\right)(\ln x)^{x}}