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Category: Integration

Question-75986

Question Number 75986 by Ajao yinka last updated on 21/Dec/19 Commented by abdomathmax last updated on 24/Dec/19 $${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({xt}\right){cos}\left({nx}\right)}{{x}}{dx}\:\:{with}\:{t}\geqslant\mathrm{0} \\ $$$${f}^{'} \left({t}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}}{\mathrm{1}+{x}^{\mathrm{2}}…

Question-75984

Question Number 75984 by Ajao yinka last updated on 21/Dec/19 Answered by mind is power last updated on 23/Dec/19 $$\mathrm{y}=\mathrm{x}^{\mathrm{2}} \\ $$$$\Rightarrow\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{log}\left(\mathrm{y}\right)}{\mathrm{4}\left(\mathrm{1}+\mathrm{y}+\mathrm{y}^{\mathrm{2}} \right)}\mathrm{dy}…