In this tutorial we shall discuss the integration of the hyperbolic secant square function, and this integral is an important integral formula. This integral belongs to the hyperbolic formulae.
The integration of the hyperbolic secant square 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 Secant Square Function
The other formulae of the hyperbolic secant square integral with an angle of hyperbolic sine in the form of a function are: