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This question already has an answer here:

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

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 .

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

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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Hint:

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 $du$

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