Question Number 35631 by abdo mathsup 649 cc last updated on 21/May/18 $${let}\:{U}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:{e}^{−\frac{{t}}{{n}}} \:\:{arctan}\left({t}\right){dt} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{U}_{{n}} \:\:\left({n}\rightarrow+\infty\right) \\ $$ Terms of Service…
Question Number 166702 by metamorfose last updated on 25/Feb/22 $$\int{e}^{{x}} {ln}\left({x}\right){dx}=..??? \\ $$ Commented by mkam last updated on 25/Feb/22 $${u}\:=\:{lnx}\:\rightarrow\:{du}\:=\:\frac{{dx}}{{x}}\:\:,\:{dv}\:=\:{e}^{{x}} \:\Rightarrow\:{v}\:=\:{e}^{{x}} \\ $$$$ \\…
Question Number 35629 by abdo mathsup 649 cc last updated on 21/May/18 $${let}\:\:{f}\left({x},{y}\right)\:=\:\int_{{x}} ^{{y}} \:\:\frac{{ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right)}{{t}}{dt}\:\:{with}\:\mathrm{0}<{x}<{y}<\mathrm{1} \\ $$$${give}\:{f}\left({x},{y}\right)\:{at}\:{form}\:{of}\:{serie}\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 35630 by abdo mathsup 649 cc last updated on 21/May/18 $$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}−{cos}\left({xt}\right)}{{t}^{\mathrm{2}} }\:{e}^{−{t}} {dt} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}−{cos}\left({t}\right)}{{t}^{\mathrm{2}} }\:{e}^{−{t}} \:{dt}\:. \\ $$…
Question Number 35628 by abdo mathsup 649 cc last updated on 21/May/18 $${find}\:{the}\:{value}\:{of}\:\:{I}\:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({t}\right){ln}\left(\mathrm{1}−{t}\right)}{{t}}{dt} \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 35627 by abdo mathsup 649 cc last updated on 21/May/18 $${study}\:{the}\:{convergence}\:{of}\: \\ $$$${I}\:\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \mid{sinx}\mid\right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$ Terms of Service Privacy…
Question Number 35625 by abdo mathsup 649 cc last updated on 21/May/18 $${find}\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\:\frac{{dx}}{\:\sqrt{\:{sin}^{\mathrm{2}} {x}\:+\xi\:{cos}^{\mathrm{2}} {x}}} \\ $$ Terms of Service Privacy Policy…
Question Number 35618 by abdo mathsup 649 cc last updated on 21/May/18 $${integrate}\:{the}\:{e}.{d}.\:{y}'\:\:+{e}^{−\mathrm{2}{x}} {y}\:=\:\left(\mathrm{2}{x}+\mathrm{1}\right){cosx} \\ $$ Commented by abdo mathsup 649 cc last updated on…
Question Number 35619 by abdo mathsup 649 cc last updated on 21/May/18 $${let}\:{f}\left({x}\right)\:=\:{x}\mid{x}\mid\:\:{odd}\:\mathrm{2}\pi\:{periodic} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 35620 by abdo mathsup 649 cc last updated on 21/May/18 $${let}\:\:{f}\left({x}\right)\:={e}^{−{x}} \:{sinx}\:\:\:{odd}\:\mathrm{2}\pi\:{periodic}\: \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$ Commented by abdo mathsup 649 cc last…