Question Number 64579 by Tawa1 last updated on 19/Jul/19 $$\int\:\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \:\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{can}\:\mathrm{we}\:\mathrm{get}\:\mathrm{a}\:\mathrm{close}\:\mathrm{form}\:\mathrm{of}\:\mathrm{this}\:\mathrm{integral}\:\mathrm{or}\:\mathrm{analytic}\:\mathrm{solution} \\ $$ Commented by mathmax by abdo last updated…
Question Number 64559 by aliesam last updated on 19/Jul/19 Commented by mathmax by abdo last updated on 20/Jul/19 $${let}\:{I}\:=\int_{\frac{\mathrm{1}}{{e}}} ^{{e}} \sqrt{\frac{\mathrm{1}−\left({lnx}\right)^{\mathrm{2}} }{{x}}}{dx}\:\Rightarrow{I}\:=\int_{\frac{\mathrm{1}}{{e}}} ^{{e}} \sqrt{\mathrm{1}−\left({lnx}\right)^{\mathrm{2}} }\frac{{dx}}{\:\sqrt{{x}}}…
Question Number 64541 by Chi Mes Try last updated on 19/Jul/19 $${lol}….{QUESTION}\:{OF}\:\:{THE}\:{DAY} \\ $$$$ \\ $$$${SHOW}\:{FULL}\:{WORKINGS} \\ $$$$ \\ $$$$\int{x}\left(\frac{\left(\mathrm{1}−{x}^{\mathrm{2}} \right){Ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)+\left(\mathrm{1}+{x}^{\mathrm{2}} \right)−\left(\mathrm{1}−{x}^{\mathrm{2}} \right){Ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{\left(\mathrm{1}−{x}^{\mathrm{4}}…
Question Number 64529 by mathmax by abdo last updated on 19/Jul/19 $${calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\frac{{dx}}{\:\sqrt{{x}}}\:\:\:{by}\:{Rieman}\:{sum}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64528 by mathmax by abdo last updated on 19/Jul/19 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{−{x}} {dx}\:\:\:{study}\:{first}\:{the}\:{convergence}. \\ $$ Commented by mathmax by abdo last updated on…
Question Number 64525 by mathmax by abdo last updated on 19/Jul/19 $${study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}} \:\:\:{with} \\ $$$${U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({nx}\right)}{{x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} }{dx}\:\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$ Commented by mathmax…
Question Number 130053 by Lordose last updated on 22/Jan/21 $$\mathrm{Show}\:\mathrm{that} \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{x}^{\mathrm{2}} \mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx}\:=\:\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$ Answered by Ar Brandon last…
Question Number 130029 by mathmax by abdo last updated on 22/Jan/21 $$\left.\mathrm{1}\right)\:\mathrm{decompose}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{4}\right)^{\mathrm{3}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\int_{\mathrm{3}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{4}\right)^{\mathrm{3}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} } \\…
Question Number 64477 by Chi Mes Try last updated on 18/Jul/19 $${pls}\:\:{i}\:{need}\:{it}\:{urgently}…\:{am}\:{stuck} \\ $$$${workings}\:{please} \\ $$$$\left(\mathrm{1}\right)\:\:\int{Ln}\left(\mathrm{1}−{Lnx}\right){dx} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\:\int\frac{\mathrm{1}}{{Lnx}}{dx} \\ $$$$ \\ $$$$\left(\mathrm{3}\right)\int\:{Ln}\left(−\mathrm{2}{Lnx}\right){dx} \\…
Question Number 130011 by mnjuly1970 last updated on 21/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\Phi=\underset{\:\:\:\:\:\mathbb{R}} {\int}{e}^{\left(−{e}^{{x}} +\mathrm{2}{x}\right)} {x}^{\mathrm{2}} {dx}=\left(\mathrm{1}−\gamma\right)^{\mathrm{2}} +\frac{\pi^{\mathrm{2}} −\mathrm{6}}{\mathrm{6}} \\ $$$$ \\ $$ Answered…