# Integral of Secant Inverse

The integral of secant inverse ${\sec ^{ - 1}}x$ it is an important integral function, but it has no direct method to find it. We shall find the integration of secant inverse by using the integration by parts method.

The integral of secant inverse is of the form

To solve this integration it must have at least two functions, however this has only one function: ${\sec ^{ - 1}}x$. So consider the second function as $1$. Now the integration becomes

The first function is ${\sec ^{ - 1}}x$ and the second function is $1$

Using the formula for integration by parts, we have

Using the formula above, equation (i) becomes

It can be written in the form

Using formula

we have

Now we can also use this integration of secant inverse as a formula.