# Solve \int \sec^n x dx for n0

## Question:

Solve {eq}\int \sec^n \ x \ dx \ {/eq} for {eq}n>0 {/eq}

## Indefinite Integral:

The indefinite integral of trigonometric functions can either be reduced to the standard form or can be applied with the trigonometric identity to form an integral in the standard result form.

As we know that the integral of:

{eq}\int \sec ^n\left(x\right)dx=\frac{\sec ^{n-1}\left(x\right)\sin \left(x\right)}{n-1}+\frac{n-2}{n-1}\int \sec ^{n-2}\left(x\right)dx\\ {/eq}

using the standard result.