# Integration of Secx Tanx

Integration of secant tangent function is an important integral formula in integral calculus; this integral belongs to trigonometric formulae.

The integration of secant tangent is of the form

To prove this formula, consider

Using the derivative formula $\frac{d}{{dx}}\sec x = \sec x\tan x$, 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 Secant Tangent Function:
The other formulas of secant tangent integral with angle is in the form of function are given as

1.

2.

Example: Evaluate the integral $\int {\sec 5x\tan 5xdx}$ with respect to $x$

We have integral

Using the formula $\int {\sec ax\tan axdx = \frac{{\sec ax}}{a}} + c$, we have