I have a fun integral for you! I know how to do it, but it is one of my favorite integrals so I figured why not share it to see what you guys come up with!

Question

anonymous · Answer

$$\int\limits_{}^{}\frac{ sinx }{ sinx + cosx }dx$$

anonymous · Answer

$\displaystyle \int\limits_{}^{}\frac{ \sin x }{ \sin x + \cos x }dx$

$\displaystyle \int\limits_{}^{}\frac{ \sin x(\sin x + \cos x) }{( \sin x + \cos x)(\sin x + \cos x) }dx$

$\displaystyle \int\limits_{}^{}\frac{ \sin^2x+\sin x  \cos x }{\sin^2x+2\sin x \cos x+\cos^2x}dx$

$\displaystyle \int\limits_{}^{}\frac{\frac{1}{2}(1-\cos (2x))+\frac{1}{2}\sin (2x) }{1+\sin(2x)}dx$

$\displaystyle \int\limits_{}^{}\frac{\frac{1}{2}-\frac{1}{2}\cos (2x)+\frac{1}{2}\sin (2x) }{1+\sin(2x)}dx$

$\displaystyle \int\limits_{}^{}\frac{\frac{1}{2}+\frac{1}{2}\sin (2x) }{1+\sin(2x)}dx-\int\limits_{}^{}\frac{\frac{1}{2}\cos (2x)}{1+\sin(2x)}dx$

$\displaystyle \frac{1}{2}\int\limits_{}^{}dx-\frac{1}{4}\int\limits_{}^{}\frac{1}{1+u}du$

yes, cool enough :)
Nice integral!