# Integral of Hyperbolic Sine

Integration of hyperbolic sine function is an important integral formula in integral calculus; this integral belongs to hyperbolic formulae.

The integration of hyperbolic sine function is of the form

To prove this formula, consider

Using the derivative formula $\frac{d}{{dx}}\cosh x = \sinh x$, we have

Integrating both sides of equation (i) with respect to $x$, we have

As we know that by definition integration is the inverse process of derivative, so the integral sign $\int {}$and $\frac{d}{{dx}}$ on the right side will cancel each other, i.e.

Other Integral Formulas of Hyperbolic Sine Function:
The other formulas of hyperbolic sine integral with angle of hyperbolic sine is in the form of function are given as
1.

2.