Question Number 144985 by imjagoll last updated on 01/Jul/21 $$\:\int\:\frac{\left(\mathrm{2}+\sqrt{\mathrm{x}}\right)}{\left(\mathrm{x}+\mathrm{1}+\sqrt{\mathrm{x}}\right)^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$ Answered by mathmax by abdo last updated on 01/Jul/21 $$\mathrm{f}\left(\mathrm{a}\right)=\int\:\:\:\frac{\mathrm{2}+\sqrt{\mathrm{x}}}{\mathrm{x}+\mathrm{a}+\sqrt{\mathrm{x}}}\:\:\:\mathrm{with}\:\mathrm{a}>\frac{\mathrm{1}}{\mathrm{4}}\:\Rightarrow\mathrm{f}^{'} \left(\mathrm{a}\right)=−\int\:\:\frac{\mathrm{2}+\sqrt{\mathrm{x}}}{\left(\mathrm{x}+\mathrm{a}+\sqrt{\mathrm{x}}\right)^{\mathrm{2}} }\mathrm{dx}\:\Rightarrow…
Question Number 144975 by mim24 last updated on 01/Jul/21 Answered by ArielVyny last updated on 01/Jul/21 $$\int{u}'×{u}^{{n}} {du}=\frac{\mathrm{1}}{{n}+\mathrm{1}}{u}^{{n}+\mathrm{1}} +{cte} \\ $$$$\int\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\left({x}+{ln}\left({x}\right)\right){dx}=\frac{\mathrm{1}}{\mathrm{2}}\left({x}+{lnx}\right)^{\mathrm{2}} \\ $$ Answered by…
Question Number 79413 by rajesh4661kumar@gmail.com last updated on 25/Jan/20 Commented by john santu last updated on 25/Jan/20 $$\left(\frac{\mathrm{cos}\:{x}\mathrm{sin}\:{x}}{\mathrm{cos}\:\mathrm{2}{x}\left(\mathrm{cos}^{\mathrm{2}} {x}−\mathrm{sin}\:^{\mathrm{2}} {x}\right)\:}\right)^{\mathrm{2}} = \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}.\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}{\mathrm{cos}\:^{\mathrm{4}} \mathrm{2}{x}}\:=\frac{\mathrm{1}}{\mathrm{4}}\mathrm{tan}\:^{\mathrm{2}}…
Question Number 144939 by yoba last updated on 30/Jun/21 $$ \\ $$$$\boldsymbol{\mathrm{resoudre}} \\ $$$$\boldsymbol{\mathrm{I}}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \boldsymbol{\mathrm{tan}}\left(\boldsymbol{\mathrm{nx}}\right)\boldsymbol{\mathrm{tan}}^{\boldsymbol{\mathrm{n}}} \left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 144925 by qaz last updated on 30/Jun/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}\right)!!}{\mathrm{2}^{\mathrm{n}} \centerdot\left(\mathrm{n}+\mathrm{1}\right)\centerdot\left(\mathrm{2n}+\mathrm{1}\right)!!}=? \\ $$ Answered by Ar Brandon last updated on 30/Jun/21 $$\left(\mathrm{2n}\right)!!=\mathrm{2n}\left(\mathrm{2n}−\mathrm{2}\right)\left(\mathrm{2n}−\mathrm{4}\right)…=\mathrm{2}^{\mathrm{n}} \mathrm{n}\left(\mathrm{n}−\mathrm{1}\right)\left(\mathrm{n}−\mathrm{2}\right)…=\mathrm{2}^{\mathrm{n}}…
Question Number 144926 by ArielVyny last updated on 30/Jun/21 $$\int_{\mathrm{0}} ^{\infty} {x}^{{n}} \left({e}^{{ix}} \right)^{{z}} {dx}=???\:\:\:\left({z}\in\mathbb{C}\right) \\ $$ Answered by mathmax by abdo last updated on…
Question Number 144924 by qaz last updated on 30/Jun/21 $$\mathrm{S}\left(\mathrm{x}\right)=\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}\right)!!}{\left(\mathrm{2n}+\mathrm{1}\right)!!}\mathrm{x}^{\mathrm{2n}} =?……..\left(\mid\mathrm{x}\mid<\mathrm{1}\right) \\ $$ Answered by Ar Brandon last updated on 30/Jun/21 $$\left(\mathrm{2n}+\mathrm{1}\right)!!=\frac{\left(\mathrm{2n}+\mathrm{1}\right)!}{\left(\mathrm{2n}\right)!!} \\…
Question Number 144909 by ArielVyny last updated on 30/Jun/21 $$\Gamma\left({a}+{ib}\right)\:{doesn}'{t}\:{exist}\:?\:{give}\:{her}\:{value} \\ $$ Answered by qaz last updated on 30/Jun/21 $$\Gamma\left(\mathrm{a}+\mathrm{ib}\right)=\int_{\mathrm{0}} ^{\infty} \mathrm{x}^{\mathrm{a}+\mathrm{ib}−\mathrm{1}} \mathrm{e}^{−\mathrm{x}} \mathrm{dx} \\…
Question Number 144905 by SLVR last updated on 30/Jun/21 Commented by SLVR last updated on 30/Jun/21 $${kindly}\:{help}\:{me} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 79373 by mathmax by abdo last updated on 24/Jan/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left({x}^{\mathrm{3}} \:+\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)} {dx} \\ $$ Terms of Service Privacy Policy Contact:…