Trigonometric Integral

Calculus Level 2

Evaluate the indefinite integral

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

Clarification: \(C\) denotes the arbitrary constant of integration.

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

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