双曲線関数の原始関数の一覧
∫ x 2 cosh  a x d x = − 2 x cosh  a x a 2 + ( x 2 a + 2 a 3 ) sinh  a x + C {\displaystyle \int x^{2}\cosh ax\,dx=-{\frac {2x\cosh ax}{a^{2}}}+\left({\frac {x^{2}}{a}}+{\frac {2}{a^{3}}}\right)\sinh ax+C\,}
∫ tanh  a x d x = 1 a ln  | cosh  a x | + C {\displaystyle \int \tanh ax\,dx={\frac {1}{a}}\ln |\cosh ax|+C\,}
∫ coth  a x d x = 1 a ln  | sinh  a x | + C {\displaystyle \int \coth ax\,dx={\frac {1}{a}}\ln |\sinh ax|+C\,}
∫ tanh n  a x d x = − 1 a ( n − 1 ) tanh n − 1  a x + ∫ tanh n − 2  a x d x (for n ≠ 1 ) {\displaystyle \int \tanh ^{n}ax\,dx=-{\frac {1}{a(n-1)}}\tanh ^{n-1}ax+\int \tanh ^{n-2}ax\,dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\,}