Question Number 85167 by mathmax by abdo last updated on 19/Mar/20 $${let}\:\varphi\left({x}\right)=\Gamma\left({x}\right).\Gamma\left(\mathrm{1}−{x}\right)\:\:{find}\:\int_{\frac{\mathrm{1}}{\mathrm{3}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} {ln}\left(\varphi\left({x}\right)\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 85162 by mathmax by abdo last updated on 19/Mar/20 $$\left.\mathrm{1}\right){find}\:\int\:{ln}\left(\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 85160 by mathmax by abdo last updated on 19/Mar/20 $$\left.\mathrm{1}\right)\:{find}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+{a}}\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{a}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{value}\:{of}\:{integrals}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}}…
Question Number 85158 by mathmax by abdo last updated on 19/Mar/20 $${calculate}\:{U}_{{n}} =\:\int_{−\frac{\mathrm{1}}{{n}}} ^{\frac{\mathrm{1}}{{n}}} \:{x}^{\mathrm{2}} \sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}{dx}\:\:\:\left({n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$ Terms of Service Privacy Policy…
Question Number 85148 by M±th+et£s last updated on 19/Mar/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}+{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{3}} +{x}^{\mathrm{7}} }\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 150678 by krauss last updated on 14/Aug/21 $$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{3}−{x}^{\mathrm{2}} } \left(\mathrm{3}−{x}^{\mathrm{2}} −{y}\right){dy}\:{dx} \\ $$ Answered by Ar Brandon last…
Question Number 150656 by mnjuly1970 last updated on 14/Aug/21 Answered by Ar Brandon last updated on 14/Aug/21 $$\Omega=\frac{\mathrm{1}}{\mathrm{2}}\left(\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)+\Gamma\left(\mathrm{1}\right)+\Gamma\left(\frac{\mathrm{3}}{\mathrm{2}}\right)\right) \\ $$$$\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\left(\sqrt{\pi}+\mathrm{1}+\frac{\sqrt{\pi}}{\mathrm{2}}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{3}\sqrt{\pi}+\mathrm{2}\right) \\ $$ Commented by mnjuly1970…
Question Number 150655 by mnjuly1970 last updated on 14/Aug/21 Answered by Ar Brandon last updated on 14/Aug/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−\sqrt{{x}}} \mathrm{ln}\left(\sqrt{{x}}\right)}{{x}^{\frac{\mathrm{1}}{\mathrm{4}}} }{dx}\underset{{x}={u}^{\mathrm{2}} } {=}\mathrm{2}\int_{\mathrm{0}} ^{\infty}…
Question Number 150647 by puissant last updated on 14/Aug/21 Answered by puissant last updated on 14/Aug/21 $${posons}\:\:{I}_{\mathrm{2}{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({sint}\right)^{\mathrm{2}{n}} {dt} \\ $$$$=\frac{\mathrm{1}×\mathrm{3}×\mathrm{5}……×\left(\mathrm{2}{n}−\mathrm{1}\right)}{\mathrm{2}×\mathrm{4}×\mathrm{6}×…..×\mathrm{2}{n}}×\frac{\pi}{\mathrm{2}} \\ $$$$\Rightarrow\:\:{I}_{\mathrm{2}{n}}…
Question Number 85097 by jagoll last updated on 19/Mar/20 $$\underset{−\pi} {\overset{\pi} {\int}}\:\mathrm{x}^{\mathrm{2020}} \:\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{8} \\ $$$$\mathrm{find}\:\underset{−\pi} {\overset{\pi} {\int}}\:\mathrm{x}^{\mathrm{2020}} \:\mathrm{cos}\:\mathrm{x}\:\mathrm{dx}\:=\:? \\ $$ Answered by john santu last…