Evaluate $\int_0^{\frac{\pi}{4}} \tan x\sec^2 x\,dx$.

Explanation

1. 01

   Put $t = \tan x$, $dt = \sec^2 x\,dx$; the limits become 0 and 1.

2. 02

   $\int_0^1 t\,dt = \frac{1}{2}$.