逆双曲線関数の原始関数の一覧
∫ arcsch  ( a x ) d x = x arcsch  ( a x ) + 1 a arcoth  1 a 2 x 2 + 1 + C {\displaystyle \int \operatorname {arcsch} (a\,x)\,dx=x\,\operatorname {arcsch} (a\,x)+{\frac {1}{a}}\,\operatorname {arcoth} {\sqrt {{\frac {1}{a^{2}\,x^{2}}}+1}}+C}
∫ x arcsch  ( a x ) d x = x 2 arcsch  ( a x ) 2 + x 2 a 1 a 2 x 2 + 1 + C {\displaystyle \int x\,\operatorname {arcsch} (a\,x)dx={\frac {x^{2}\,\operatorname {arcsch} (a\,x)}{2}}+{\frac {x}{2\,a}}{\sqrt {{\frac {1}{a^{2}\,x^{2}}}+1}}+C}