Question Number 27400 by Tinkutara last updated on 06/Jan/18 $${Evaluate}\:\underset{{r}} {\overset{\mathrm{0}} {\int}}\sqrt{\frac{{x}}{{r}−{x}}}\:{dx} \\ $$ Commented by Tinkutara last updated on 07/Jan/18 $${But}\:{this}\:{integral}\:{was}\:{used}\:{in}\:{a}\:{Physics} \\ $$$${question}\:{where}\:{its}\:{value}\:{can}'{t}\:{be} \\…
Question Number 92937 by mathmax by abdo last updated on 09/May/20 $${find}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{dx}}{\mathrm{3}{cosx}\:+\mathrm{2}} \\ $$ Commented by mathmax by abdo last updated on 10/May/20…
Question Number 92936 by mathmax by abdo last updated on 09/May/20 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{dx}}{{cosx}\:+{sinx}} \\ $$ Commented by abdomathmax last updated on 10/May/20 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{2}\pi}…
Question Number 92934 by mathmax by abdo last updated on 09/May/20 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{xlnx}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92935 by mathmax by abdo last updated on 09/May/20 $${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{\left({x}^{\mathrm{2}} −\mathrm{3}\right){dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 27392 by A1B1C1D1 last updated on 06/Jan/18 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{integral}: \\ $$$$ \\ $$$$\int\:\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } \:\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Can}'\mathrm{t}\:\mathrm{be}\:\mathrm{calculated}\:\mathrm{trivially}. \\ $$ Terms of Service…
Question Number 92925 by frc2crc last updated on 09/May/20 $${S}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{4}{k}^{\mathrm{2}} −\mathrm{1}\right)^{{n}} } \\ $$$${find}\:{a}\:{simpler}\:{form} \\ $$ Commented by mr W last updated…
Question Number 158420 by akolade last updated on 03/Nov/21 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{lnx}}{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by puissant last updated on 03/Nov/21 $$\Omega=\int_{\mathrm{0}} ^{\infty} \frac{{lnx}}{\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 92889 by i jagooll last updated on 09/May/20 $$\mathrm{learning}\:\mathrm{distancing} \\ $$$$\int\:\mathrm{ln}\left(\sqrt{\mathrm{1}+\mathrm{x}}+\sqrt{\mathrm{1}−\mathrm{x}}\right)\:\mathrm{dx} \\ $$ Commented by john santu last updated on 09/May/20 $$\mathrm{u}\:=\:\mathrm{ln}\left(\sqrt{\mathrm{1}+\mathrm{x}}\:+\sqrt{\mathrm{1}−\mathrm{x}}\right) \\…
Question Number 27345 by abdo imad last updated on 05/Jan/18 $${prove}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{x}−\mathrm{1}} }{{e}^{{t}} −\mathrm{1}}{dt}\:\:=\xi\left({x}\right)\Gamma\left({x}\right) \\ $$$${with}\:\xi\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\propto} \:\frac{\mathrm{1}}{{n}^{{x}} }\:\:\:{and}\:\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} {dt} \\…