<s>[INST] How Evaluate This Integral $\int x‎^{‎3‎} ‎‎\sin ‎2x ‎dx‎$? 
How can find the following indefinite integral?
  $$\int x‎^{‎3‎}  ‎‎\sin ‎2x ‎dx‎$$

Thanks For the Help!
 [/INST] Hint: Integration by parts:
$\int_{x} x^{3}\sin 2x = \frac{-1}{2} \int_{x} x^{3} D\cos 2x = \frac{-1}{2}\cos (2x)x^{3} + \frac{3}{2} \int_{x} \cos (2x) x^{2} + \text{some constant}$; $\int_{x}\cos (2x)x^{2} = \frac{1}{2}\int_{x}x^{2}D\sin 2x = \frac{1}{2}\sin (2x)x^{2} - \frac{1}{2}\int_{x} \sin (2x)2x + \text{some constant}$.
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