Question

Solve: $I=\int (3\sin x{\cos }^{2}x-{\sin }^{3}x)dx$ is equal to ?

• A. $I=\frac{\cos 3x}{3}+C$
• B. $I=-\frac{\cos 3x}{3}+C$
• C. $I=\frac{\sin 3x}{3}+C$
• D. $I=-\frac{\sin 3x}{3}+C$

Answer 1

The correct option is B $I=-\frac{\cos 3x}{3}+C$

$\int \left(3\sin x\right(1-{\sin }^{2}x)-{\sin }^{3}x)dx$
$=\int (3\sin x-3{\sin }^{3}x-{\sin }^{3}x)dx$
$=\int (3\sin x-4{\sin }^{3}x)dx$
$=\int \sin \left(3x\right)dx$
$=-\frac{\cos 3x}{3}+C$