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