Xem thêm: Danh sách tích phân với hàm hyperbol

∫ sinh ⁡ a x d x = a − 1 cosh ⁡ a x + C {\displaystyle \int \sinh ax\,dx=a^{-1}\cosh ax+C} ∫ cosh ⁡ a x d x = a − 1 sinh ⁡ a x + C {\displaystyle \int \cosh ax\,dx=a^{-1}\sinh ax+C} ∫ tanh ⁡ a x d x = a − 1 ln ⁡ ( cosh ⁡ a x ) + C {\displaystyle \int \tanh ax\,dx=a^{-1}\ln(\cosh ax)+C} ∫ coth ⁡ a x d x = a − 1 ln ⁡ ( sinh ⁡ a x ) + C {\displaystyle \int \coth ax\,dx=a^{-1}\ln(\sinh ax)+C} ∫ d u a 2 + u 2 = sinh − 1 ⁡ ( u a ) + C {\displaystyle \int {\frac {du}{\sqrt {a^{2}+u^{2}}}}=\sinh ^{-1}\left({\frac {u}{a}}\right)+C} ∫ d u u 2 − a 2 = cosh − 1 ⁡ ( u a ) + C {\displaystyle \int {\frac {du}{\sqrt {u^{2}-a^{2}}}}=\cosh ^{-1}\left({\frac {u}{a}}\right)+C} ∫ d u a 2 − u 2 = a − 1 tanh − 1 ⁡ ( u a ) + C ; u 2 < a 2 {\displaystyle \int {\frac {du}{a^{2}-u^{2}}}=a^{-1}\tanh ^{-1}\left({\frac {u}{a}}\right)+C;u^{2}<a^{2}} ∫ d u a 2 − u 2 = a − 1 coth − 1 ⁡ ( u a ) + C ; u 2 > a 2 {\displaystyle \int {\frac {du}{a^{2}-u^{2}}}=a^{-1}\coth ^{-1}\left({\frac {u}{a}}\right)+C;u^{2}>a^{2}} ∫ d u u a 2 − u 2 = − a − 1 sech − 1 ⁡ ( u a ) + C {\displaystyle \int {\frac {du}{u{\sqrt {a^{2}-u^{2}}}}}=-a^{-1}\operatorname {sech} ^{-1}\left({\frac {u}{a}}\right)+C} ∫ d u u a 2 + u 2 = − a − 1 csch − 1 ⁡ | u a | + C {\displaystyle \int {\frac {du}{u{\sqrt {a^{2}+u^{2}}}}}=-a^{-1}\operatorname {csch} ^{-1}\left|{\frac {u}{a}}\right|+C}

với C là hằng số tích phân.