# Not able to integrate $\int \frac{\sin x}{\sin x + \cos x} \ dx$ ?? [duplicate]

$$\int \frac{\sin x}{\sin x + \cos x} \ dx$$

So what I thought of doing was converting $$\sin x$$ and $$\cos x$$ into $$\tan\frac{x}{2}$$

But it got converted into non integrable form

Any other methods would be appreciated .

## marked as duplicate by GNUSupporter 8964民主女神 地下教會, Parcly Taxel, Jyrki Lahtonen, xbh, Key FlexOct 7 '18 at 17:07

Let $$I=\int \frac {\sin x}{\sin x+\cos x}dx$$ And $$J=\int \frac {\cos x}{\sin x+\cos x}dx$$
$$J+I$$ is pretty easy. For $$J-I$$ put $$\sin x+\cos x= u$$ to get numerator of $$J-I$$ as $$du$$