# Integral of Inverse Cosecant

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

The integral of inverse cosecant is of the form

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

The first function is ${\csc ^{ - 1}}x$ 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 inverse cosecant as a formula.