Question Number 138598 by qaz last updated on 15/Apr/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}!\left(\mathrm{2}{n}+\mathrm{3}\right)}\left(\frac{\mathrm{4}}{\pi}\right)^{{n}} =? \\ $$ Answered by mr W last updated on 15/Apr/21 $${e}^{{x}}…
Question Number 138580 by Bekzod Jumayev last updated on 15/Apr/21 Commented by Bekzod Jumayev last updated on 15/Apr/21 $${Please}\:{help}? \\ $$$$ \\ $$ Answered by…
Question Number 7506 by gourav~ last updated on 01/Sep/16 $$\int\left\{\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}+\sqrt{{x}}}\right\}^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{{dx}}{{x}}=? \\ $$$$ \\ $$$$ \\ $$ Answered by Yozzia last updated on 01/Sep/16 $${Let}\:{I}=\int\frac{\mathrm{1}}{{x}}\sqrt{\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}+\sqrt{{x}}}}{dx}.…
Question Number 73037 by aliesam last updated on 05/Nov/19 Commented by mathmax by abdo last updated on 06/Nov/19 $$\left.\mathrm{1}\right)\:{I}_{\mathrm{0}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{\mathrm{1}−{x}} {dx}\:=\left[−{e}^{\mathrm{1}−{x}} \right]_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 138570 by bemath last updated on 15/Apr/21 $$\underset{\:\sqrt{\mathrm{2}}} {\overset{\mathrm{2}} {\int}}\:\frac{{dx}}{{x}^{\mathrm{2}} \:\sqrt{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} }}\:=?\: \\ $$ Answered by Ar Brandon last updated on 15/Apr/21…
Question Number 7482 by kishanjith last updated on 31/Aug/16 $$\int\frac{\left(\mathrm{1}+{x}\right)^{−\mathrm{2}/\mathrm{3}} }{\left(\mathrm{1}+{x}\right)}{dx} \\ $$ Answered by sandy_suhendra last updated on 31/Aug/16 $$=\int\left(\mathrm{1}−{x}\right)^{\frac{−\mathrm{5}}{\mathrm{3}}} {dx} \\ $$$${let}\:\:\:{U}=\mathrm{1}−{x}\: \\…
Question Number 73012 by vishalbhardwaj last updated on 05/Nov/19 $$\int\sqrt{{tan}\mathrm{x}}\:{d}\mathrm{x} \\ $$ Answered by mind is power last updated on 05/Nov/19 $$\mathrm{u}=\sqrt{\mathrm{tan}\left(\mathrm{x}\right)} \\ $$$$\Rightarrow\mathrm{x}=\mathrm{arctan}\left(\mathrm{u}^{\mathrm{2}} \right)\Rightarrow\mathrm{dx}=\frac{\mathrm{2u}}{\mathrm{1}+\mathrm{u}^{\mathrm{4}}…
Question Number 138533 by Ñï= last updated on 14/Apr/21 $$\int_{\mathrm{0}} ^{\mathrm{5}} \left(\mathrm{1}+{x}\right)\delta\left({x}^{\mathrm{2}} −\mathrm{4}\right){dx}=? \\ $$ Commented by Lordose last updated on 14/Apr/21 $$\delta\:\Rightarrow\:\mathrm{Meaning}? \\ $$…
Question Number 7465 by Yozzia last updated on 30/Aug/16 $$\int\frac{{t}^{\mathrm{3}} }{\left({t}−\mathrm{1}\right)^{\mathrm{2}} \left({t}^{\mathrm{2}} +{t}+\mathrm{1}\right)^{\mathrm{2}} }{dt}=? \\ $$ Commented by prakash jain last updated on 30/Aug/16 $$=\int\frac{{t}^{\mathrm{3}}…
Question Number 72988 by mathmax by abdo last updated on 05/Nov/19 $${calculate}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{e}^{−{xt}^{\mathrm{2}} } }{\mathrm{4}+{t}^{\mathrm{2}} }{dt}\:\:\:{with}\:{x}>\mathrm{0} \\ $$ Commented by mathmax by abdo last…