# Secant Integral Formula

In this tutorial we will prove the formula of secant integral which is also an important formula in integral calculus; this integral belongs to the category of trigonometric integral formulae.

The integration of secant function is of the form

To prove this formula, consider

By multiplying and dividing the relation $\left( {\sec x + \tan x} \right)$

Here $f\left( x \right) = \sec x + \tan x$, then $f'\left( x \right) = \sec x\tan x + {\sec ^2}x$

Now using the formula of integration $\int {\frac{{f'\left( x \right)}}{{f\left( x \right)}}dx = \ln f\left( x \right) + c}$, we have

Now further we can solve this result as follows,

So in conclusion we can write this formula as

Other Integral Formulas of Secant Function:
The other formulas of secant integral with angle of sine is in the form of function are given as

1.

2.