Find $\int\nolimits^{\frac{\pi}{4}}_{0} ( \tan^3{x} ) \space dx$ given $2\tan^3x = \frac{d}{dx}( \tan^2x+2\ln \cos x )$
$\int\nolimits^{\frac{\pi}{4}}_{0} \tan^3{x} \space dx = \frac{1}{2}\left[\tan^2{x} + 2 \ln{\cos{x}}\right]^{\frac{\pi}{4}}_0$
I could go on but $\cos{\frac{\pi}{4}}$ is a decimal. Answer is $\frac{1}{2}(1 - \ln{2})$. How do I simplify down to that