Question

Solve :-
$\int \frac{\cos 2x}{{\left(\sin x+\cos x\right)}^2}dx$

Answer 1

Now,

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

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

$=\int \frac{\cos 2x}{1+\sin 2x}dx$

$=\frac{1}{2}\int \frac{d(1+\sin 2x)}{1+\sin 2x}$

$=\frac{1}{2}\log |(1+\sin 2x)|+c$. [ Where $c$ is integrating constant]