Question Number 66347 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} {ln}\left({x}\right)}{{x}^{\mathrm{2}} −\mathrm{1}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{the}\:{existence}\:{of}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{I}_{{n}+\mathrm{1}} −{I}_{{n}} \\ $$$$\left.\mathrm{3}\left.\right){prove}\:{thst}\:{x}\in\right]\mathrm{0},\mathrm{1}\left[\:\Rightarrow\mathrm{0}<\frac{{xlnx}}{{x}^{\mathrm{2}} −\mathrm{1}}<\frac{\mathrm{1}}{\mathrm{2}}\right.…
Question Number 66345 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+\mathrm{2}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 66344 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{f}_{{n}} \left({x}\right)=\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{{n}} \right)^{\mathrm{1}+\frac{\mathrm{1}}{{n}}} }\:\:\:{defined}\:{on}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\left.\mathrm{1}\right){prove}\:{that}\:{f}_{{n}} \rightarrow^{{cs}} \:\:{to}\:{a}\:{function}\:{f}\:{on}\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} {f}_{{n}} \left({x}\right){dx}…
Question Number 66340 by mathmax by abdo last updated on 12/Aug/19 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} \left(\mathrm{2}−{x}\right)}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 66338 by mathmax by abdo last updated on 12/Aug/19 $${find}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{5}}{\mathrm{4}}} \:\:\:\frac{{x}^{\mathrm{3}} {dx}}{\:\sqrt{\mathrm{2}+{x}−{x}^{\mathrm{2}} }} \\ $$ Commented by mathmax by abdo last updated…
Question Number 131875 by mnjuly1970 last updated on 09/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}.. \\ $$$$\:\:\:\:\:\Phi=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({cosh}\left({x}\right)\right)}{{cosh}\left({x}\right)}{dx}=??? \\ $$ Answered by mindispower last updated on 09/Feb/21 $$=\int_{\mathrm{1}} ^{\infty}…
Question Number 66339 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\frac{{dx}}{\:\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}}+\sqrt{\mathrm{4}{x}^{\mathrm{2}} \:+\mathrm{1}}} \\ $$ Commented by Prithwish sen last updated on…
Question Number 131874 by mnjuly1970 last updated on 09/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{calculus}\:… \\ $$$$\:\:\:\phi\:=\int_{\mathrm{0}} ^{\:\infty} \frac{{tanh}^{\mathrm{2}} \left({x}\right){dx}}{{x}^{\mathrm{2}} }\:=? \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 66336 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tanx}}{\:\sqrt{\mathrm{2}}{cosx}\:+\mathrm{2}{sin}^{\mathrm{2}} {x}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66337 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:\int_{−\mathrm{7}} ^{−\mathrm{3}} \:\:\frac{\left({x}−\mathrm{1}\right){dx}}{\:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}{x}−\mathrm{3}}} \\ $$ Commented by Prithwish sen last updated on 13/Aug/19…