Question

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

Answer 1

We are given, $I=\int \left(\frac{1-sinx}{x+cosx}\right)dx$

Let $x+cosx=t$

now, diferentiate with respect $x.$ we get,

$[1+(-sinx\left)\right]dx=dt$

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

$=ln\left|t\right|+c$

$I=ln|x+cosx|+c$