双曲線関数の原始関数の一覧
also: ∫ cosh n  a x sinh m  a x d x = − cosh n + 1  a x a ( m − 1 ) sinh m − 1  a x + n − m + 2 m − 1 ∫ cosh n  a x sinh m − 2  a x d x (for m ≠ 1 ) {\displaystyle \int {\frac {\cosh ^{n}ax}{\sinh ^{m}ax}}dx=-{\frac {\cosh ^{n+1}ax}{a(m-1)\sinh ^{m-1}ax}}+{\frac {n-m+2}{m-1}}\int {\frac {\cosh ^{n}ax}{\sinh ^{m-2}ax}}dx\qquad {\mbox{(for }}m\neq 1{\mbox{)}}\,}
also: ∫ cosh n  a x sinh m  a x d x = − cosh n − 1  a x a ( m − 1 ) sinh m − 1  a x + n − 1 m − 1 ∫ cosh n − 2  a x sinh m − 2  a x d x (for m ≠ 1 ) {\displaystyle \int {\frac {\cosh ^{n}ax}{\sinh ^{m}ax}}dx=-{\frac {\cosh ^{n-1}ax}{a(m-1)\sinh ^{m-1}ax}}+{\frac {n-1}{m-1}}\int {\frac {\cosh ^{n-2}ax}{\sinh ^{m-2}ax}}dx\qquad {\mbox{(for }}m\neq 1{\mbox{)}}\,}