Question

Integrate the following function: $\frac{\sin x}{1+\cos x}$

Answer 1

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

Let $1+\cos x=t$

Differentiating w.r.t $x,$ we have

$\Rightarrow -\sin xdx=dt$

$\Rightarrow \int \frac{-dt}{t}=-\log (1+\cos x)+c$

$=\log \left(\frac{1}{1+\cos x}\right)+c.$

Hence, the answer is $\log \left(\frac{1}{1+\cos x}\right)+c.$