Question

Evaluate: $\int \frac{1+\cos x}{x+\sin x}dx$.

Answer 1

Now,

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

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

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