Question

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

• A. $x+\sin x+C$
• B. $x-\sin x+C$
• C. $\sin x+C$
• D. $\cos x+C$

Answer 1

The correct option is B $x-\sin x+C$

$\int \frac{{\sin }^{2}x}{1+\cos x}dx$
$=\int \frac{1-{\cos }^{2}x}{1+\cos x}dx$
$=\int \frac{(1-\cos x)(1+\cos x)}{1+\cos x}dx$
$=\int (1-\cos x)dx$
$=x-\sin x+C$