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Question Number 166614 by qaz last updated on 23/Feb/22

calculate::   ∫_0 ^∞ (({x}^2 (1−{x})^2 )/((1+x)^5 ))=(7/(12))−γ

$$\mathrm{calculate}::\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\left\{\mathrm{x}\right\}^{\mathrm{2}} \left(\mathrm{1}−\left\{\mathrm{x}\right\}\right)^{\mathrm{2}} }{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{5}} }=\frac{\mathrm{7}}{\mathrm{12}}−\gamma \\ $$

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