The integration of coshx is equal to sinhx+C. Here we learn how to integrate coshx, the cosine hyperbolic function.

The integration formula of cosh(x) is given as follows:

∫coshx dx = sinhx +C

where C denotes an integral constant.

## How to Integrate coshx

**Question:** What is the integral of coshx? That is,

Find ∫coshx dx.

*Answer:*

By the definition of cosine hyperbolic functions, it is known that

coshx = $\dfrac{e^x+e^{-x}}{2}$

Integrating both sides, the integral of coshx will be equal to

∫coshx dx = $\int \dfrac{e^x+e^{-x}}{2}$ +C, where C is an arbitrary constant.

= $\dfrac{1}{2}$ ∫(e^{x} + e^{-x}) dx + C

= $\dfrac{1}{2}$ [∫e^{x} dx + ∫e^{-x} dx] + C

= $\dfrac{1}{2}$ [e^{x} + (-e^{-x})] + C, because ∫e^{mx} dx = e^{mx}/m for any integer m.

= $\dfrac{e^x-e^{-x}}{2}$ + C

= sinh(x) +C, as we know that sinh(x) = (e^{x} – e^{-x})/2.

Therefore, the integration of cosh(x) is equal to sinh(x)+C, that is, ∫cosh(x) dx = sinh(x) +C where C is an integral constant.

**Also Read:**

Integration of sinh(x) | Integration of tan x |

Integration of cot x | Derivative of cosh(x) |

Derivative of tanh(x) | Derivative of sinh(x) |

## FAQs

**Q1: What is the integration of coshx?**

Answer: The integration of coshx is equal to sinhx+C, that is, ∫coshx dx = sinhx +C.