Show that \(\displaystyle\int_0^{\dfrac{\pi}{4}}x\tan^2(x)\,\mathrm{d}x=\dfrac{\pi}{32}(8-\pi)-

Question

Show that $\displaystyle\int_0^{\dfrac{\pi}{4}}x\tan^2(x)\,\mathrm{d}x=\dfrac{\pi}{32}(8-\pi)-\ln\sqrt2$.

Accepted Answer

$\dfrac{\pi}{32}(8-\pi)-\ln\sqrt2$

Mixed Integration Techniques