Question Number 99261 by Ar Brandon last updated on 19/Jun/20 $$\mathrm{Given}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\mathrm{f}\left(\mathrm{t}\right)\mathrm{dt} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{F}\:\mathrm{is}\:\mathrm{defined},\:\mathrm{continuous},\:\mathrm{and}\:\mathrm{derivable}. \\ $$$$\mathrm{And}\:\mathrm{find}\:\mathrm{its}\:\mathrm{derivative} \\ $$ Answered by abdomathmax last updated on 19/Jun/20 $$\mathrm{F}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\mathrm{2}}\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\:\int^{\mathrm{x}}…
Question Number 33705 by math khazana by abdo last updated on 22/Apr/18 $${let}\:\:\alpha>\mathrm{0}\:\:{find}\:{the}\:{fourier}\:{transform}\:{of} \\ $$$${f}\left({t}\right)\:=\:{e}^{−{a}^{\mathrm{2}} {t}^{\mathrm{2}} } \\ $$ Commented by math khazana by abdo…
Question Number 33703 by math khazana by abdo last updated on 22/Apr/18 $${give}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{x}\:{e}^{−{x}} }{\mathrm{1}\:−{e}^{−\mathrm{2}{x}} }\:{sin}\left(\pi{x}\right){dx}\:\:{at}\:{form}\:{of}\:{serie}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 33704 by math khazana by abdo last updated on 22/Apr/18 $${let}\:{f}\left({t}\right)\:=\:\frac{\mathrm{1}}{{a}^{\mathrm{2}} \:+{t}^{\mathrm{2}} }\:\:{witha}>\mathrm{0}\:{give}\:{the}\:{fourier} \\ $$$${transformfor}\:{f}\:. \\ $$$$ \\ $$ Commented by prof Abdo…
Question Number 99239 by abdomathmax last updated on 19/Jun/20 $$\mathrm{calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by MJS last updated on 19/Jun/20 $$\mathrm{Ostrogradski}\:\mathrm{gives}…
Question Number 99234 by abdomathmax last updated on 19/Jun/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{x}} \mathrm{lnx}\:\mathrm{dx} \\ $$ Answered by maths mind last updated on 19/Jun/20 $$\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\infty}…
Question Number 33695 by math khazana by abdo last updated on 22/Apr/18 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{e}^{−\frac{{x}}{{n}}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}. \\ $$ Commented by math khazana by…
Question Number 99228 by M±th+et+s last updated on 19/Jun/20 $$ \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{sin}\left({x}\right){ln}\left({x}\right)}{{x}}{dx}=\frac{−\gamma\pi}{\mathrm{2}} \\ $$ Answered by maths mind last updated on 20/Jun/20 $$\frac{{ln}\left({x}\right)}{{x}}=\frac{\partial}{\partial{a}}{x}^{{a}−\mathrm{1}}…
Question Number 33694 by math khazana by abdo last updated on 22/Apr/18 $${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{{n}} \:\:+{e}^{{x}} }\:\:. \\ $$ Commented by math khazana by…
Question Number 33689 by NECx last updated on 22/Apr/18 $$\int\frac{{x}}{{x}^{\mathrm{3}} +\mathrm{1}}{dx} \\ $$ Commented by mondodotto@gmail.com last updated on 22/Apr/18 $$\boldsymbol{\mathrm{let}}\:\boldsymbol{\mathrm{u}}=\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\mathrm{1} \\ $$$$\frac{\boldsymbol{\mathrm{du}}}{\boldsymbol{\mathrm{dx}}}=\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \Rightarrow\boldsymbol{\mathrm{dx}}=\frac{\boldsymbol{\mathrm{du}}}{\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}}…