Question

Evaluate:

$\int \frac{2\sin x}{\sin x+\cos x}dx$.

Answer 1

Now,

$\int \frac{2\sin x}{\sin x+\cos x}dx$

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

$=\int dx$$-\int \frac{d(\sin x+\cos x)}{\sin x+\cos x}dx$

$=x-\log |(\sin x+\cos x)|+c$ [ Where $c$ is integrating constant]