Question Number 65015 by aliesam last updated on 24/Jul/19 $$\int\frac{\sqrt{{x}+\mathrm{1}}\:−\:\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}+\mathrm{1}}\:+\:\sqrt{{x}−\mathrm{1}}}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 24/Jul/19 $${let}\:{I}\:=\int\:\:\frac{\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}}{\:\sqrt{{x}+\mathrm{1}}+\sqrt{{x}−\mathrm{1}}}{dx}\:\Rightarrow{I}\:=\int\:\frac{\left(\sqrt{{x}+\mathrm{1}}−\sqrt{{x}−\mathrm{1}}\right)^{\mathrm{2}} }{{x}+\mathrm{1}−{x}+\mathrm{1}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\:\int\:\left({x}+\mathrm{1}−\mathrm{2}\sqrt{{x}^{\mathrm{2}}…
Question Number 130544 by EDWIN88 last updated on 26/Jan/21 $$\:\int\:\frac{\mathrm{sin}\:^{\mathrm{2}} {x}\:\mathrm{sec}\:^{\mathrm{2}} {x}\:+\mathrm{2}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:\mathrm{tan}\:{x}\:\mathrm{sin}^{−\mathrm{1}} {x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} {x}\right)}\:{dx}? \\ $$ Answered by mindispower last updated on 26/Jan/21…
Question Number 65003 by mathmax by abdo last updated on 24/Jul/19 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\Gamma\left({x}\right)}\:\:{with}\:\:\Gamma\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\:\:\:\left({x}>\mathrm{0}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 65004 by mathmax by abdo last updated on 24/Jul/19 $${let}\:{U}_{{n}} =\:\int_{\frac{\mathrm{1}}{{n}}} ^{\frac{\mathrm{2}}{{n}}} \:\Gamma\left({x}\right)\Gamma\left(\mathrm{1}−{x}\right){dx}\:\:\:\:{with}\:{n}\geqslant\mathrm{3} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{and}\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Commented by mathmax…
Question Number 130536 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)\mathrm{d}\theta \\ $$ Answered by Ar Brandon last updated on 26/Jan/21…
Question Number 130534 by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{7}} \:\mathrm{arctan}\left(\mathrm{2x}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{calculate}\:\:\mathrm{f}^{\left(\mathrm{4}\right)} \left(\mathrm{0}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{7}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{5}\right)} \left(\mathrm{1}\right) \\ $$ Answered by mathmax…
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 $$…