Prove that`int_0^(pi/4) 2tan^3xdx=1-log2`

Explanation

`=int_0^(pi/4) 2tanx.tan^2xdx`

`=int_0^(pi/4) 2tanx(sec^2x−1)`

`=int_0^(pi/4)2tanxsec^2xdx−int_0^(pi/4) 2tanx.dx`

`=2(2tan^2x)/2∣−2logsecx∣`

`=1−2(logsqrt(2)
−2log1)`

`=1−log2`