Answer
$$ \displaystyle\int {x}^{2}{\cdot}\sin\left(x\right){\cdot}x{\cdot}\sin\left(x\right)\, \mathrm d x = -{{4\,x^3\,\sin \left(2\,x\right)-6\,x\,\sin \left(2\,x\right)+6\,x ^2\,\cos \left(2\,x\right)-3\,\cos \left(2\,x\right)-2\,x^4}\over{16 }} $$
Explanation
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