Question Number 62937 by Prithwish sen last updated on 27/Jun/19 $$\int_{\mathrm{0}} ^{\:\:\mathrm{x}} \frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 27/Jun/19…
Question Number 62930 by mathmax by abdo last updated on 27/Jun/19 $${find}\:{the}\:{value}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{\sqrt{{x}}} {dx}\:\left({study}\:{first}\:{the}\:{convergence}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128471 by mnjuly1970 last updated on 07/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:{calculus}\:… \\ $$$$\:\:\:\:\:\:\:\Phi\overset{?} {=}\int_{\mathrm{0}} ^{\:\mathrm{1}} \left({ln}\left({x}\right)\right)^{\mathrm{2}} {ln}\left(\sqrt{−{ln}\left({x}\right)}\:{dx}\right. \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 62912 by Hope last updated on 26/Jun/19 Answered by Hope last updated on 27/Jun/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62908 by aliesam last updated on 26/Jun/19 $$\int\frac{{arctan}\left({x}\right)}{{x}}{dx} \\ $$ Commented by mathmax by abdo last updated on 26/Jun/19 $$\left.\:\left.{for}\:{all}\:{x}\:{from}\:{R}\:\:\:\:{u}\rightarrow\frac{{arctanu}}{{u}}{is}\:{integrable}\:{on}\:\right]\mathrm{0},{x}\right]{let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{{x}} \:\frac{{arctan}\left({tu}\right)}{{u}}{du} \\…
Question Number 62906 by Prithwish sen last updated on 26/Jun/19 $$\int\mathrm{x}^{\mathrm{x}} \mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 27/Jun/19 $${let}\:{A}\:=\int\:{x}^{{x}} \:{dx}\:\Rightarrow{A}\:=\int\:{e}^{{xln}\left({x}\right)}…
Question Number 128417 by liberty last updated on 07/Jan/21 $$\:\:\:\:\:\:\:\:\:\eta\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{x}^{\mathrm{3}} \:\left(\mathrm{1}−\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{n}−\mathrm{1}} \:\mathrm{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 07/Jan/21…
Question Number 128408 by bramlexs22 last updated on 07/Jan/21 $$\rho\:=\:\int\:\frac{\mathrm{sin}\:\left(\mathrm{4}{x}\right)}{\mathrm{sin}\:^{\mathrm{4}} \left({x}\right)+\mathrm{cos}\:^{\mathrm{4}} \left({x}\right)}\:{dx}\: \\ $$ Answered by mr W last updated on 07/Jan/21 $$=\int\frac{\mathrm{sin}\:\left(\mathrm{4}{x}\right)}{\mathrm{1}−\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \:{x}\:\mathrm{cos}^{\mathrm{2}} \:{x}}{dx}…
Question Number 62856 by mathmax by abdo last updated on 26/Jun/19 $${let}\:{f}\left(\lambda\right)\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{x}^{\mathrm{4}} }{{x}^{\mathrm{6}} \:+\lambda^{\mathrm{6}} }\:{dx}\:\:\:{with}\:\lambda>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{f}\left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{also}\:{g}\left(\lambda\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{4}} }{\left({x}^{\mathrm{6}} \:+\lambda^{\mathrm{6}}…
Question Number 62855 by mathmax by abdo last updated on 26/Jun/19 $${find}\:\int\:\:\left(\frac{{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{6}} }\right)^{\mathrm{2}} \:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}^{\mathrm{8}} }{\left(\mathrm{1}+{x}^{\mathrm{6}} \right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{+\infty}…