Question Number 33744 by prof Abdo imad last updated on 23/Apr/18 $${let}\:\:{P}_{{n}} \left({x}\right)=\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)….\left(\mathrm{1}+{x}^{\mathrm{2}^{{n}} } \right) \\ $$$${calculate}\:\:{lim}_{{n}\rightarrow+\infty} \int_{\mathrm{0}} ^{{x}} \:{P}_{{n}} \left({t}\right){dt}\:\:{with}\:\:\mathrm{0}<{x}<\mathrm{1}\:. \\ $$…
Question Number 164809 by mathlove last updated on 22/Jan/22 $$\left.\mathrm{1}\right)\:\:\:\:\int\frac{\sqrt[{\mathrm{3}}]{{x}}}{\:\sqrt{{x}}+\sqrt[{\mathrm{4}}]{{x}}}=? \\ $$$$\left.\mathrm{2}\right)\:\:\:\:\int\frac{{x}}{\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}} }=? \\ $$ Answered by Ar Brandon last updated on 22/Jan/22 $$\mathrm{Ostrogradsky}…
Question Number 33737 by prof Abdo imad last updated on 23/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({xt}\right)}{\left({t}^{\mathrm{2}} \:+\:{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dt}\:. \\ $$ Commented by prof Abdo imad last…
Question Number 33736 by prof Abdo imad last updated on 23/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}+{x}\:+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$ Commented by prof Abdo imad last…
Question Number 33735 by prof Abdo imad last updated on 22/Apr/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{cos}\left(\mathrm{2}{x}\right){dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left(\:\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}\right)}\:. \\ $$ Commented by prof Abdo imad last updated…
Question Number 99261 by Ar Brandon last updated on 19/Jun/20 $$\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}…