Question

How do you find the integral of `int sec^n(x)` if m or n is an integer?

Answer 1

See Explanation

Explanation:

The proof for this is pretty lengthy, but I've found a good explanation showing it here: https://www.enotes.com/homework-help/integral-sec-n-x-dx-722738

In essence, it comes down to this formula (also known as integral reduction)

`intsec^ndx=(sec^(n-1)sinx)/(n-1)+(n-2)/(n-1)intsec^(n-2)dx`