Question Number 65354 by mathmax by abdo last updated on 28/Jul/19 $${find}\:\:\int\:\:\:\:\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} +{x}−\mathrm{2}}} \\ $$$$ \\ $$ Commented by mathmax by abdo last updated on…
Question Number 65352 by mathmax by abdo last updated on 28/Jul/19 $${give}\:{the}\:{integralA}_{{n}} =\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dt}}{\mathrm{1}+{x}^{{n}} }\:\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2} \\ $$$${at}\:{form}\:{of}\:{serie}. \\ $$ Commented by mathmax by abdo…
Question Number 65332 by aliesam last updated on 28/Jul/19 Commented by mathmax by abdo last updated on 29/Jul/19 $${let}\:{suppose}\:{n}\:{inter}\:{let}\:{decompose}\:{the}\:{fraction} \\ $$$${F}\left({x}\right)\:=\frac{{x}}{{x}^{{n}} \:+\mathrm{1}} \\ $$$${z}^{{n}} \:+\mathrm{1}\:=\mathrm{0}\:\Rightarrow{z}^{{n}}…
Question Number 65320 by hovea cw last updated on 28/Jul/19 Commented by mathmax by abdo last updated on 28/Jul/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+{x}}{lnxdx}\:{changement}\:\sqrt{\mathrm{1}+{x}}={t}\:{give}\:\mathrm{1}+{x}\:={t}^{\mathrm{2}} \:\Rightarrow \\ $$$${x}\:={t}^{\mathrm{2}}…
Question Number 65321 by hovea cw last updated on 28/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 65319 by hovea cw last updated on 28/Jul/19 Commented by mathmax by abdo last updated on 28/Jul/19 $${those}\:{integrals}\:{are}\:{solved}\:\:{see}\:{the}\:{platform}. \\ $$ Commented by mathmax…
Question Number 130844 by mnjuly1970 last updated on 29/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:\:\:{advanced}\:\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{3}}} \frac{{dx}}{\:\sqrt[{\mathrm{3}}]{{cos}^{\mathrm{2}} \left({x}\right)}}\:=\frac{\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{3}}} \sqrt{\pi}}{\:\sqrt{\mathrm{3}}} \\ $$ Answered by Dwaipayan Shikari last…
Question Number 65307 by divyajyoti last updated on 28/Jul/19 $$\int\frac{\left(\mathrm{4}{x}+\mathrm{3}\right){dx}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{3}}}\:=\:?\: \\ $$ Answered by divyajyoti last updated on 28/Jul/19 $$=\int\frac{{dt}}{\:\sqrt{{t}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\int\frac{{dx}}{\:\sqrt{\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\sqrt{\mathrm{7}}}{\mathrm{2}}\right)^{\mathrm{2}} }} \\ $$$$=\mathrm{2}\sqrt{\mathrm{2}{x}^{\mathrm{2}}…
Question Number 130845 by mnjuly1970 last updated on 29/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$\:\:{calculate}:: \\ $$$$\:\:\:{lim}_{\:{n}\rightarrow\infty} \underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{k}}{\mathrm{2}{n}^{\mathrm{2}} +{k}}\:=? \\ $$$$ \\ $$ Answered by Ar…
Question Number 130835 by mathmax by abdo last updated on 29/Jan/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{4}} \right)}{\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on…