Question Number 130532 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{find}\:\mathrm{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{1}+\alpha\mathrm{x}\right)}{\mathrm{4}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\:\:\left(\alpha>\mathrm{0}\right) \\ $$$$\mathrm{and}\:\mathrm{determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{arctan}\left(\mathrm{1}+\mathrm{2x}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}}\mathrm{dx} \\ $$ Terms of Service…
Question Number 130530 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{xsin}\left(\mathrm{2x}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 130533 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{find}\:\int\:\:\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{5}}{\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{2}} −\mathrm{3}}\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21…
Question Number 130531 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{arctan}\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)\mathrm{dx} \\ $$ Answered by Lordose last updated on 26/Jan/21 $$…
Question Number 130528 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{calculate}\:\int_{\mathrm{2}} ^{\infty} \:\:\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{5}} } \\ $$ Answered by mathmax by abdo last updated…
Question Number 64994 by aliesam last updated on 23/Jul/19 $$\int\sqrt{{tanh}\left({x}\right)}\:{dx} \\ $$ Commented by zakaria elghaouti last updated on 24/Jul/19 Answered by zakaria elghaouti last…
Question Number 130529 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{calvulste}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{\mathrm{cos}\left(\mathrm{2x}\right)}{\mathrm{3}+\mathrm{cosx}}\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on 27/Jan/21…
Question Number 64993 by mathmax by abdo last updated on 23/Jul/19 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({x}^{\mathrm{2}} \right)−{sin}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({x}^{\mathrm{2}}…
Question Number 130512 by MJS_new last updated on 26/Jan/21 $$\int{x}\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{2}{x}}} {dx}=? \\ $$ Commented by Dwaipayan Shikari last updated on 26/Jan/21 $$\frac{\mathrm{1}}{\mathrm{2}{x}}=−{t}\Rightarrow\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }=\frac{{dt}}{{dx}} \\ $$$$=−\mathrm{2}\int{x}^{\mathrm{3}}…
Question Number 64975 by Tawa1 last updated on 23/Jul/19 Commented by Prithwish sen last updated on 23/Jul/19 $$\int\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} .\mathrm{2}!}\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}!}+….} \mathrm{dx}\:=\int\mathrm{x}^{\sqrt{\mathrm{e}}−\mathrm{1}} \mathrm{dx}\:\mathrm{and}\:\mathrm{proceed} \\ $$ Terms…