Question Number 131891 by Raxreedoroid last updated on 09/Feb/21 $$\int\:\frac{{x}!}{\:\sqrt{{x}}}\:{dx}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66350 by mathmax by abdo last updated on 12/Aug/19 $${study}\:{the}\:{convergence}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\left(\mathrm{1}−\sqrt{\frac{{x}^{{n}} }{\mathrm{2}+{x}^{{n}} }}\right){dx}\:\:\:\:{n}\in{N} \\ $$ Commented by mathmax by abdo last updated…
Question Number 66348 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{nature}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dx}}{{e}^{{x}} −{cosx}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66351 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{{nt}} }{\left(\mathrm{1}+{e}^{{t}} \right)^{{n}+\mathrm{1}} }{dt}\:\:\:\:\:\left({n}\:{from}\:{N}^{\bigstar} \right) \\ $$$$\left.\right){prove}\:{the}\:{existence}\:{of}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:{I}_{{n}} \\…
Question Number 66346 by mathmax by abdo last updated on 12/Aug/19 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}^{\mathrm{7}} }{{t}^{\mathrm{16}} \:+\mathrm{1}}{dt} \\ $$ Commented by mathmax by abdo last updated…
Question Number 66349 by mathmax by abdo last updated on 12/Aug/19 $${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{arctan}\left({x}−\mathrm{1}\right)}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} }{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 66347 by mathmax by abdo last updated on 12/Aug/19 $${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…