Indefinite integral of trigonometric function

Calculus Level 1

Determine the indefinite integral of the following expression: $\sin{2x}\left(5-\frac{3}{2}\sin^4{x}\right) .$

Details and assumptions

Use $C$ as the constant of integration.

2\sin^2{x} - \frac{1}{3} \sin^6{x} + C

4\sin^2{x} - \frac{1}{6} \sin^6{x} + C

3\sin^2{x} - \frac{1}{4} \sin^6{x} + C

5\sin^2{x} - \frac{1}{2} \sin^6{x} + C