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Question Number 141244 by ajfour last updated on 17/May/21 $${I}=\int_{\mathrm{0}} ^{\:\infty} \frac{{x}\left\{\left({a}^{\mathrm{2}} −{b}^{\mathrm{2}} \right){x}−\mathrm{2}{a}^{\mathrm{2}} {x}^{\mathrm{2}} −\mathrm{2}{b}^{\mathrm{2}} \right\}{dx}}{\left({a}^{\mathrm{2}} {x}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)^{\mathrm{2}} \left\{\left({a}^{\mathrm{2}} −{b}^{\mathrm{2}} \right){x}+{a}^{\mathrm{2}} {x}^{\mathrm{2}} +{b}^{\mathrm{2}}…
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