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Answer
$$ \int {10}{x}^{{3}}-{5}\frac{{x}}{\sqrt{{{x}^{{4}}-{x}^{{2}}+{6}}}} \, d\,x = -{{5\,\left({\rm asinh}\; \left({{2\,x^2-1}\over{\sqrt{23}}}\right) -x^4\right)}\over{2}} $$
Explanation
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