Trigonometric Integral

Calculus Level 2

Evaluate the indefinite integral

$\int (1 + \cos x)^3 \, dx.$

Clarification: $C$ denotes the arbitrary constant of integration.

\frac{1}{12} \sin 3x + \frac{3}{4} \sin 2x\\ + \frac{15}{4} \sin x + \frac{5}{2} x + C

\frac{1}{12} \cos 3x + \frac{3}{4} \cos 2x\\ - \frac{15}{4} \cos x + \frac{5}{2} x + C

\frac{1}{12} \cos 3x + \frac{3}{4} \cos 2x\\ + \frac{15}{4} \cos x + \frac{5}{2} x + C

\frac{1}{12} \sin 3x + \frac{3}{4} \sin 2x\\ - \frac{15}{4} \sin x + \frac{5}{2} x + C