Question Number 171130 by 119065 last updated on 08/Jun/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 171125 by mnjuly1970 last updated on 08/Jun/22 Answered by mindispower last updated on 09/Jun/22 $$=\Sigma\Sigma\frac{{mn}}{{n}\mathrm{3}^{{n}} +{m}\mathrm{3}^{{n}} }\left(\frac{{m}\mathrm{3}^{{n}} +{n}\mathrm{3}^{{m}} }{\mathrm{3}^{{m}+{n}} }\right) \\ $$$$=\mathrm{2}{S} \\…
Question Number 171117 by meetbhavsar25 last updated on 08/Jun/22 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{sin}\:{x}}{{x}}{dx}\:=\:\left(?\right) \\ $$ Answered by aleks041103 last updated on 08/Jun/22 $${f}\left({z}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{zx}} \frac{{sinx}}{{x}}{dx}…
Question Number 40044 by abdo mathsup 649 cc last updated on 15/Jul/18 $${let}\:{f}\left({t}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\:{cosx}\:+{t}\:{sinx}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({t}\right)\:{then}\:{find}\:\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({cosx}\:+\mathrm{2}\:{sinx}\right){dx} \\…
Question Number 40043 by abdo mathsup 649 cc last updated on 15/Jul/18 $${find}\:\:{the}\:{value}\:{of}\:\:\int_{−\mathrm{1}} ^{+\infty} \:\:\sqrt{{x}+\mathrm{1}}{e}^{−{x}} \:{dx} \\ $$$$ \\ $$$$ \\ $$ Answered by prof…
Question Number 171108 by akolade last updated on 08/Jun/22 Answered by qaz last updated on 08/Jun/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{x}^{\mathrm{3}} −\mathrm{2x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{5}} }{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{7}} }\mathrm{dx}=\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{3}}…
Question Number 105574 by bemath last updated on 30/Jul/20 $$\int\:\frac{{x}−\mathrm{1}}{{x}+{x}^{\mathrm{2}} \mathrm{ln}\:{x}}\:{dx}\:?\: \\ $$ Answered by bobhans last updated on 30/Jul/20 $${set}\:{x}\:={e}^{{u}} ,\:{dx}\:=\:{e}^{{u}} {du} \\ $$$${I}=\int\:\frac{\left({e}^{{u}}…
Question Number 105565 by mathmax by abdo last updated on 30/Jul/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\mathrm{2}} \mathrm{ln}\left(\mathrm{1}−\mathrm{x}^{\mathrm{3}} \right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\mathrm{calculate}\:\int\:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Answered…
Question Number 171096 by Kalebwizeman last updated on 07/Jun/22 $$ \\ $$$$\int\frac{{x}\:{e}^{\mathrm{2}{x}} }{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:\:\:{please}\:{help} \\ $$ Answered by thfchristopher last updated on 07/Jun/22 $$\int\frac{{x}\:{e}^{\mathrm{2}{x}} }{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}}…
Question Number 171090 by Kodjo last updated on 07/Jun/22 $${I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{u}\right)\sqrt{{ud}\left({u}\right)} \\ $$$${Demonstrate}\:{that}\:\forall{n}\in{N},\:{I}_{{n}+\mathrm{1}} −{I}_{{n}} =\left(\mathrm{1}−{u}\right)^{{n}} {u}^{\frac{\mathrm{3}}{\mathrm{2}}} {d}\left({u}\right)\:\:{and}\:{deduce}\:{the}\:{meaning}\:{of}\:{variations}\:{of}\:\left({I}_{{n}} \right)\in{N} \\ $$ Commented by Kodjo…