2)\int \frac{sinx.cosx}{(sinx+cosx)} dx =\frac{1}{2}\int \frac{(sinx+cosx)^2-1}{sinx+cosx} dx
\frac{1}{2} \left ( \int \left ( sinx+cosx \right )dx -\int \frac{dx}{sinx+cosx} \right ){ }
\frac{1}{2}\left ( \int sinx\, dx + \int cosx\, dx + \int \frac{dx}{sinx+cosx}\right )
\frac{1}{2}\left ( -cosx+ sinx-\frac{1}{\sqrt{2}}\ln \left | \tan\left ( \frac{x}{2} + \frac{1}{2}\tan^{-1}(1) |\right )
\frac{1}{2}\left ( -cosx+ sinx-\frac{1}{\sqrt{2}}\ln \left | \tan\left ( \frac{x}{2} + \frac{\pi }{8} \right )\right |\right )+c