Question

Find the integral of the function: $\frac{{\sin }^{2}x}{1+\cos x}$

Answer 1

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

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

$=\int \frac{(1-\cos x)(1+\cos x)}{1+\cos x}dx$

$=\int (1-\cos x)dx$

$=\int 1.dx-\int \cos x.dx$

$=x-\sin x+C$

Where $C$ is constant of integration.