Question

How do you evaluate `int tan^4xsec^2xdx`?

Answer 1

Part of the integrand is the derivative of another part. Try substitution.

Explanation:

Let `u = tanx`, then `du = sec^2 x dx`, and we have

`int u^4 du = 1/5 u^5 +C = 1/5 tan^5x +C`