Question

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

Answer 1

Let $t=x+\sin x\Rightarrow dt=(1+\cos x)dx$

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

$=\int \frac{dt}{t}$

$=\log t+c$

$=\log (x+\sin x)+c$ where $c$ is the constant of integration.