対数関数の原始関数の一覧
∫ ln  x n d x x = ( ln  x n ) 2 2 n (for n ≠ 0 ) {\displaystyle \int {\frac {\ln {x^{n}}\;dx}{x}}={\frac {\left(\ln {x^{n}}\right)^{2}}{2n}}\qquad {\mbox{(for }}n\neq 0{\mbox{)}}}
∫ ln  x d x x m = − ln  x ( m − 1 ) x m − 1 − 1 ( m − 1 ) 2 x m − 1 (for m ≠ 1 ) {\displaystyle \int {\frac {\ln x\,dx}{x^{m}}}=-{\frac {\ln x}{(m-1)x^{m-1}}}-{\frac {1}{(m-1)^{2}x^{m-1}}}\qquad {\mbox{(for }}m\neq 1{\mbox{)}}}
∫ ( ln  x ) n d x x m = − ( ln  x ) n ( m − 1 ) x m − 1 + n m − 1 ∫ ( ln  x ) n − 1 d x x m (for m ≠ 1 ) {\displaystyle \int {\frac {(\ln x)^{n}\;dx}{x^{m}}}=-{\frac {(\ln x)^{n}}{(m-1)x^{m-1}}}+{\frac {n}{m-1}}\int {\frac {(\ln x)^{n-1}dx}{x^{m}}}\qquad {\mbox{(for }}m\neq 1{\mbox{)}}}