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}} \\ $$$$ \\ $$$${A}=\mathrm{ln}\left({x}+{n}\right)\:\mid_{\mu} ^{\mu+\epsilon} \\ $$$$=\mathrm{ln}\left(\mu+\epsilon+{n}\right)−\mathrm{ln}\left(\mu+{n}\right) \\ $$$$=\mathrm{ln}\left(\frac{\mu+\epsilon+{n}}{\mu+{n}}\right) \\ $$$$=\mathrm{ln}\left(\frac{\mu+{n}}{\mu+{n}}+\frac{\epsilon}{\mu+{n}}\right) \\ $$$$…
Question Number 68532 by Faradtimmy last updated on 13/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 134058 by john_santu last updated on 27/Feb/21 $$\mathcal{J}\:=\:\int\:\frac{{dx}}{\mathrm{1}+\mathrm{tan}\:{x}+\mathrm{csc}\:{x}+\mathrm{cot}\:{x}+\mathrm{sec}\:{x}} \\ $$ Answered by john_santu last updated on 27/Feb/21 $$\mathcal{J}=\int\:\frac{{dx}}{\mathrm{1}+\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}+\frac{\mathrm{1}}{\mathrm{sin}\:{x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}+\frac{\mathrm{1}}{\mathrm{cos}\:{x}}} \\ $$$$\:=\:\int\:\frac{\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}\mathrm{cos}\:{x}+\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{sin}\:{x}} \\…
Question Number 134038 by Raxreedoroid last updated on 27/Feb/21 Answered by EDWIN88 last updated on 27/Feb/21 $$\mathrm{V}=\mathrm{2}\pi\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\left(\mathrm{5}−\mathrm{x}\right)\left(\mathrm{8}−\mathrm{x}^{\mathrm{3}} \right)\:\mathrm{dx} \\ $$$$\:\mathrm{V}=\mathrm{2}\pi\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\left(\mathrm{40}−\mathrm{5x}^{\mathrm{3}} −\mathrm{8x}+\mathrm{x}^{\mathrm{4}}…
Question Number 134039 by Raxreedoroid last updated on 27/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 134016 by mnjuly1970 last updated on 26/Feb/21 $$ \\ $$$$\:\:\:\:\:\:?{prove}\::\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} {H}_{\mathrm{2}{n}} }{\mathrm{2}{n}+\mathrm{1}}=\frac{\pi}{\mathrm{8}}{ln}\left(\mathrm{2}\right).. \\ $$ Answered by mnjuly1970 last updated on 27/Feb/21…