Question

How do you integrate `∫sec^2 (x) tan^3 (x)dx`?

Answer 1

Derivative of `tanx` is `sec^2x` , so use substitution.

`intsec^2xtan^3xdx=int(tanx)^3sec^2xdx`.

You can probably figure it out from there, but just in case:

Let `u=tanx`, then `du=sec^2xdx`, so the integral becomes `intu^3du`, which, of course, evaluates to `1/4tan^4x+C`.