Question Number 108303 by Sayantan chakraborty last updated on 16/Aug/20
$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\frac{\mathrm{1}}{\left({sinx}+{cosx}\right)}{sin}^{\mathrm{6}} {x}\:{dx}\:{equals} \\ $$
Answered by Sayantan chakraborty last updated on 16/Aug/20
$$\mathrm{Answer}:\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{ln}\left(\sqrt{}\mathrm{2}+\mathrm{1}\right)+\mathrm{1}\right). \\ $$