$\frac{d}{dx}\left(\left(x^5-10x^2-10\right)\left(x^2-2\right)\right)=\left(5x^{4}-20x\right)\left(x^2-2\right)+2\left(x^5-10x^2-10\right)x$
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Integral
$\int\left(x^5-10x^2-10\right)\left(x^2-2\right)dx=\frac{x^{8}}{8}-\frac{1}{3}x^{6}-2x^{5}+\frac{10}{3}x^{3}+20x+C_0$
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