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