The integration of the hyperbolic sine function is an important integral formula in integral calculus. This integral belongs to the hyperbolic formulae.
The integration of the hyperbolic sine function is of the form
To prove this formula, consider
Using the derivative formula , we have
Integrating both sides of equation (i) with respect to , we have
As we know that by definition integration is the inverse process of the derivative, so the integral sign and on the right side will cancel each other out, i.e.
Other Integral Formulae of the Hyperbolic Sine Function
The other formulae of the hyperbolic sine integral with the angle of hyperbolic sine in the form of function are: