Hyperbolic functions: \(\sinh x,\) \(\cosh x,\) \(\tanh x,\) \(\text{coth }x,\) \(\text{sech }x,\) \(\text{csch }x\)

Argument (independent variable): \(x\)

Real number: \(C\)

Real number: \(C\)

- Integral involving hyperbolic sine

\({\large\int\normalsize} {\sinh x\,dx} =\) \( \cosh x + C\) - Integral involving hyperbolic cosine

\({\large\int\normalsize} {\cosh x\,dx} =\) \( \sinh x + C\) - Integral involving hyperbolic tangent

\({\large\int\normalsize} {\tanh x\,dx} =\) \( \ln\cosh x + C\) - Integral involving hyperbolic cotangent

\({\large\int\normalsize} {\text {coth }x\,dx} =\) \(\ln \left| {\sinh x} \right| + C\) - Integral involving hyperbolic secant squared

\({\large\int\normalsize} {{\text {sech}^2}x\,dx} =\) \( \tanh x + C\) - Integral involving hyperbolic cosecant squared

\({\large\int\normalsize} {{\text {csch}^2}x\,dx} =\) \( -\text{coth }x + C\) - \({\large\int\normalsize} {\text {sech }x \tanh x\,dx} =\) \( -\text{sech }x + C\)
- \({\large\int\normalsize} {\text {csch }x \,\text {coth }x\,dx} =\) \( -\text{csch }x + C\)