Question Number 10790 by Nur450737 last updated on 25/Feb/17 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{\mathrm{sin}\:{x}}\:{dx} \\ $$ Answered by bahmanfeshki last updated on 26/Feb/17 $$\sqrt{\mathrm{sin}\:{x}}={t} \\ $$$${t}^{\mathrm{2}} =\mathrm{sin}\:{x}\Rightarrow\mathrm{cos}\:{x}=\sqrt{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 141859 by iloveisrael last updated on 24/May/21 $$\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{4}{e}^{−{x}^{\mathrm{2}} } }{\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dx}\: \\ $$ Commented by Dwaipayan Shikari last updated on…
Question Number 76323 by aliesam last updated on 26/Dec/19 Commented by mind is power last updated on 27/Dec/19 $$\mathrm{I}_{\mathrm{n}} =\int\mathrm{cos}^{\mathrm{n}} \left(\mathrm{x}\right)\mathrm{e}^{\mathrm{ax}} \mathrm{dx} \\ $$$$\mathrm{by}\:\mathrm{part} \\…
Question Number 76317 by Master last updated on 26/Dec/19 Commented by john santu last updated on 26/Dec/19 $$\int{e}^{{xlnx}} \:{dx}.\:{with}\:{integration}\:{by}\:{part} \\ $$$${u}={e}^{{xlnx}} \rightarrow{du}=\left({lnx}+\mathrm{1}\right){e}^{{xlnx}} .\:{dv}={dx}\: \\ $$$${I}={xe}^{{xlnx}}…
Question Number 141848 by iloveisrael last updated on 24/May/21 $$\:\mathscr{I}\:=\:\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }−\mathrm{1}}\:{dx}\: \\ $$ Answered by ArielVyny last updated on 24/May/21 $${we}\:{know}\:{that}\:\:{cos}^{\mathrm{2}} {x}+{sin}^{\mathrm{2}} {x}=\mathrm{1} \\ $$$${let}\:{us}\:{consider}\:{that}\:\:{x}={sint}…
Question Number 141847 by iloveisrael last updated on 24/May/21 $$\:\mathcal{I}\:=\:\int\:\frac{\mathrm{sec}\:{x}}{\mathrm{1}+\mathrm{csc}\:{x}}\:{dx}\: \\ $$ Answered by MJS_new last updated on 24/May/21 $$\int\frac{\mathrm{sec}\:{x}}{\mathrm{1}+\mathrm{csc}\:{x}}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\:\rightarrow\:{dx}=\mathrm{2cos}^{\mathrm{2}} \:\frac{{x}}{\mathrm{2}}\:{dt}\right] \\ $$$$=−\mathrm{4}\int\frac{{t}}{\left({t}−\mathrm{1}\right)\left({t}+\mathrm{1}\right)^{\mathrm{3}}…
Question Number 76298 by benjo last updated on 26/Dec/19 $$\int\sqrt{\:\mathrm{tanx}+\mathrm{cotxdx}} \\ $$ Commented by benjo last updated on 26/Dec/19 Commented by john santuy last updated…
Question Number 10761 by 2525 last updated on 24/Feb/17 $$\mathrm{Express}\:\mathrm{the}\:\mathrm{following}\:\Gamma\:\mathrm{function}\:\mathrm{using}\:\mathrm{tables} \\ $$$$\mathrm{and}\:\mathrm{evaluate}\:\mathrm{them}\:\mathrm{using}\:\mathrm{a}\:\mathrm{table}\:\mathrm{or}\:\Gamma\:\mathrm{functions}. \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} {x}^{−\mathrm{1}/\mathrm{3}} {e}^{−\mathrm{8}{x}\:} {dx} \\ $$ Terms of Service…
Question Number 141811 by mnjuly1970 last updated on 23/May/21 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\Theta:=\left(\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{n}^{\mathrm{4}} }{\mathrm{2}^{{n}} \:.\:{n}!}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} =? \\ $$ Answered by qaz last updated on…
Question Number 141757 by Ndala last updated on 23/May/21 $$\Gamma\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)=\frac{\sqrt{\pi}\centerdot\Gamma\left(\mathrm{2n}+\mathrm{1}\right)}{\mathrm{2}^{\mathrm{2n}} \Gamma\left(\mathrm{n}+\mathrm{1}\right)} \\ $$ Commented by Ndala last updated on 23/May/21 $$\mathrm{someone}\:\mathrm{to}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{the}\:\mathrm{proof}.\:\mathrm{Please} \\ $$ Terms of…