What is the integral of int tan^3x secxdx?

1 Answer
Jan 18, 2016

int tan^3x secx dx = 1/3 sec^3x-secx +C. If you really want the integral of that integral ask and we'll see what we can do.

Explanation:

Useful facts:

d/dx(secx) = secxtanx

tan^2x = sec^2x-1

int tan^3x secx dx = int(sec^2x-1)secxtanx dx

Let u = secx, so that du = secxtanxdx.

The integral then is int(u^2-1) du.

The student should be able to finish from here.