Question Number 134185 by mnjuly1970 last updated on 28/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…..{advanced}\:\:\:{calculus}…. \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\:{i}:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{cos}\left({tan}\left({x}\right)−{x}\right)}{{cos}\left({x}\right)}{dx}=\frac{\pi}{{e}} \\ $$$$\:\:\:\:{ii}:\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}{e}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)^{{n}^{\mathrm{2}} } =\frac{\pi}{{e}\sqrt{{e}}} \\ $$$$\:\:…
Question Number 134182 by Algoritm last updated on 28/Feb/21 Answered by Ñï= last updated on 01/Mar/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)^{\mathrm{3}} \frac{\left(\mathrm{1}+{x}\right)}{\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 68600 by Abdo msup. last updated on 14/Sep/19 $$\left.\mathrm{1}\right){calculatef}\left({a}\right)=\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({arctanx}\right)}{{a}+{x}^{\mathrm{2}} }{dx}\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)?{calculste}\:\:{g}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({arctanx}\right)}{\left({a}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{if}\:{integrals} \\ $$$$\int_{\mathrm{0}} ^{\infty}…
Question Number 68598 by Abdo msup. last updated on 14/Sep/19 $$\:{find}\:\int\:\:\:\:\frac{{dx}}{{x}^{\mathrm{3}} −\mathrm{4}{x}\:+\mathrm{3}} \\ $$ Commented by turbo msup by abdo last updated on 14/Sep/19 $${let}\:{I}\:=\int\:\:\frac{{dx}}{{x}^{\mathrm{3}}…
Question Number 68596 by Abdo msup. last updated on 14/Sep/19 $${calculate}\:\int_{\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\:\frac{{xdx}}{\mathrm{3}+{cosx}} \\ $$ Commented by mathmax by abdo last updated on 15/Sep/19 $${changeent}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give}…
Question Number 68594 by Abdo msup. last updated on 14/Sep/19 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{dx}}{{cosx}\:+{sin}\left(\mathrm{2}{x}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 68597 by Abdo msup. last updated on 14/Sep/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left({e}^{{x}^{\mathrm{2}} } \right)}{{x}^{\mathrm{2}} \:+\mathrm{8}}{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 68595 by Abdo msup. last updated on 14/Sep/19 $${calculate}\:\:{A}_{\lambda} =\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{e}^{−\lambda{x}^{\mathrm{2}} } }{{x}^{\mathrm{4}} +\mathrm{1}}{dx}\:\:{with}\:\lambda>\mathrm{0}\:\:{and}\: \\ $$$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{A}_{\lambda} \:{d}\lambda \\ $$ Commented…
Question Number 3046 by Filup last updated on 03/Dec/15 $$\int_{\mathrm{0}} ^{\:{n}} {x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\centerdot\centerdot\centerdot\left({x}+{n}\right){dx}=? \\ $$$$\left({x},\:{n}\right)\in\mathbb{R} \\ $$ Commented by Filup last updated on 04/Dec/15 $${x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\centerdot\centerdot\centerdot\left({x}+{n}\right)=\frac{\left({x}+{n}\right)!}{\left({x}−\mathrm{1}\right)!} \\…
Question Number 3017 by Filup last updated on 03/Dec/15 $${A}=\int_{\mu} ^{\:\mu+\epsilon} \:\frac{{dx}}{{x}+{n}} \\ $$$$ \\ $$$${A}=\mathrm{ln}\left({x}+{n}\right)\:\mid_{\mu} ^{\mu+\epsilon} \\ $$$$=\mathrm{ln}\left(\mu+\epsilon+{n}\right)−\mathrm{ln}\left(\mu+{n}\right) \\ $$$$=\mathrm{ln}\left(\frac{\mu+\epsilon+{n}}{\mu+{n}}\right) \\ $$$$=\mathrm{ln}\left(\frac{\mu+{n}}{\mu+{n}}+\frac{\epsilon}{\mu+{n}}\right) \\ $$$$…