Question

Integrate with respect to $x$:
$\frac{1-\sin x}{x+\cos x}$

Answer 1

Let $I=\int \frac{1-\sin x}{x+\cos x}dx$

Put $x+\cos x=t$, then, $\left(1-\sin x\right)dx=dt$

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

$=\log t+c$

$=\log \left(x+\cos x\right)+c$