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