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

The sinh(x) integral formula is given below:

∫sinhx dx = coshx +C

where C is an integration constant.

## How to Integrate sinhx

**Question:** Find the integral of sinhx, that is,

Find ∫sinhx dx.

*Answer:*

One know that

sinhx = $\dfrac{e^x-e^{-x}}{2}$

Integrating both sides, we get that

∫sinhx dx = $\int \dfrac{e^x-e^{-x}}{2}$ +C. Here C is a 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

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

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

**Also Read:**

Integration of sec 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 sinhx?**

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