Integration of the secant tangent function is an important integral formula in integral calculus, and this integral belongs to the trigonometric formulae.
The integration of secant tangent 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, the integral sign and on the right side will cancel each other out, i.e.
Other Integral Formulae of the Secant Tangent Function
The other formulae of secant tangent integral with an angle in the form of a function are given as
Example: Evaluate the integral with respect to
We have integral
Using the formula , we have