対数関数の原始関数の一覧
{\displaystyle \int {\frac {dx}{x^{n}\ln x}}=\ln \left|\ln x\right|+\sum _{k=1}^{\infty }(-1)^{k}{\frac {(n-1)^{k}(\ln x)^{k}}{k\cdot k!}}}
∫ d x x ( ln  x ) n = − 1 ( n − 1 ) ( ln  x ) n − 1 (for n ≠ 1 ) {\displaystyle \int {\frac {dx}{x(\ln x)^{n}}}=-{\frac {1}{(n-1)(\ln x)^{n-1}}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}}
∫ ln  ( x 2 + a 2 ) d x = x ln  ( x 2 + a 2 ) − 2 x + 2 a tan − 1  x a {\displaystyle \int \ln \left(x^{2}+a^{2}\right)\;dx=x\ln \left(x^{2}+a^{2}\right)-2x+2a\tan ^{-1}{\frac {x}{a}}}
∫ x x 2 + a 2 ln  ( x 2 + a 2 ) d x = 1 4 ln 2  ( x 2 + a 2 ) {\displaystyle \int {\frac {x}{x^{2}+a^{2}}}\ln \left(x^{2}+a^{2}\right)\;dx={\frac {1}{4}}\ln ^{2}\left(x^{2}+a^{2}\right)}