# Integrals of Hyperbolic Functions

• Hyperbolic functions: $$\sinh x,$$ $$\cosh x,$$ $$\tanh x,$$ $$\text{coth }x,$$ $$\text{sech }x,$$ $$\text{csch }x$$
Argument (independent variable): $$x$$
Real number: $$C$$
1. Integral involving hyperbolic sine
$${\large\int\normalsize} {\sinh x\,dx} =$$ $$\cosh x + C$$
2. Integral involving hyperbolic cosine
$${\large\int\normalsize} {\cosh x\,dx} =$$ $$\sinh x + C$$
3. Integral involving hyperbolic tangent
$${\large\int\normalsize} {\tanh x\,dx} =$$ $$\ln\cosh x + C$$
4. Integral involving hyperbolic cotangent
$${\large\int\normalsize} {\text {coth }x\,dx} =$$ $$\ln \left| {\sinh x} \right| + C$$
5. Integral involving hyperbolic secant squared
$${\large\int\normalsize} {{\text {sech}^2}x\,dx} =$$ $$\tanh x + C$$
6. Integral involving hyperbolic cosecant squared
$${\large\int\normalsize} {{\text {csch}^2}x\,dx} =$$ $$-\text{coth }x + C$$
7. $${\large\int\normalsize} {\text {sech }x \tanh x\,dx} =$$ $$-\text{sech }x + C$$
8. $${\large\int\normalsize} {\text {csch }x \,\text {coth }x\,dx} =$$ $$-\text{csch }x + C$$