Question

$\int \frac{{\sin }^{2}x}{1+\cos x}dx$

Answer 1

$$\begin{gathered} \int \frac{{\sin }^{2}x}{1+\cos x}dx \\ =\int \frac{\left(1-{\cos }^{2}x\right)}{\left(1+\cos x\right)}dx \\ =\int \frac{\left(1-\cos x\right)\left(1+\cos x\right)}{\left(1+\cos x\right)}dx \\ =\int \left(1-\cos x\right)dx \\ =x-\sin x+\mathrm{C} \end{gathered}$$