Question Number 42305 by maxmathsup by imad last updated on 22/Aug/18 $${let}\:{f}\left({x}\right)\:=\:\int_{−\infty} ^{+\infty} \:\:\frac{{cos}\left({xt}\right)}{\left({t}−{i}\right)^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{let}\:{R}\:={Re}\left({f}\left({x}\right)\right)\:{and}\:{I}\:={Im}\left({f}\left({x}\right)\right)\:{extract}\:{R}\:{and}\:{I} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{R}\:{and}\:{I} \\ $$$$\left.\mathrm{3}\right)\:{conclude}\:{the}\:{value}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\mathrm{2}{t}\right)}{\left({t}−{i}\right)^{\mathrm{2}}…
Question Number 42260 by math khazana by abdo last updated on 21/Aug/18 $${let}\:{f}\left({a}\right)\:=\:\int_{−\infty} ^{+\infty} \:{cos}\left({ax}^{\mathrm{2}} \right){dx}\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right)\:{interms}\:{of}\:{a} \\ $$$$\left.\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\:{cos}\left(\mathrm{2}{x}^{\mathrm{2}} \right){dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{−\infty}…
Question Number 107790 by Ar Brandon last updated on 12/Aug/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$ Commented by prakash jain last updated on 12/Aug/20 $$\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 42232 by maxmathsup by imad last updated on 20/Aug/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{d}\theta}{\left(\mathrm{1}+{cos}\theta\right)^{\mathrm{3}} } \\ $$ Answered by MJS last updated on 21/Aug/18 $$\mathrm{simply}\:\mathrm{Weierstrass}…
Question Number 42228 by rahul 19 last updated on 20/Aug/18 $$\mathrm{Solve}\:: \\ $$$$\mathrm{2}{x}^{\mathrm{2}} {ydx}\:−\mathrm{2}{y}^{\mathrm{4}} {dx}+\mathrm{2}{x}^{\mathrm{3}} {dy}+\mathrm{3}{xy}^{\mathrm{3}} {dy}=\mathrm{0}. \\ $$ Answered by ajfour last updated on…
Question Number 42222 by maxmathsup by imad last updated on 20/Aug/18 $${let}\:{f}\left({x}\right)\:={e}^{−\mid{x}\mid} \:,\:\:\mathrm{2}\pi\:{periodic}\:{even}\:\:{developp}\:{f}\:{at}\:{fourier}\:{serie}\:. \\ $$ Answered by maxmathsup by imad last updated on 21/Aug/18 $${f}\left({x}\right)=\frac{{a}_{\mathrm{0}}…
Question Number 42221 by rahul 19 last updated on 20/Aug/18 $$\mathrm{Solve}: \\ $$$$\frac{\mathrm{dt}}{\mathrm{d}{x}}\:=\:\frac{\mathrm{2}}{{x}+\mathrm{t}}\:. \\ $$ Answered by MrW3 last updated on 20/Aug/18 $${u}={x}+{t} \\ $$$$\frac{{du}}{{dx}}=\mathrm{1}+\frac{{dt}}{{dx}}…
Question Number 107756 by bemath last updated on 12/Aug/20 $$\:\frac{\mathcal{B}{e}\mathcal{M}{ath}}{\coprod} \\ $$$$\:\int\:{x}^{\mathrm{2}} \:\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{3}\right)\:{dx}\: \\ $$ Answered by hgrocks last updated on 12/Aug/20 $$ \\…
Question Number 42215 by rahul 19 last updated on 20/Aug/18 $$\mathrm{Number}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{lines}\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\frac{\mathrm{dy}}{{dx}}\:+\:{x}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} −\:{y}\:=\mathrm{0}\:{is}\:? \\ $$ Commented by rahul 19 last updated on…
Question Number 42191 by maxmathsup by imad last updated on 19/Aug/18 $${let}\:{A}_{{p}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sin}\left({px}\right)}{{e}^{{x}} −\mathrm{1}}\:{dx}\:\:{with}\:{p}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){give}\:{A}_{{p}} \:\:{at}\:{form}\:{of}\:{serie} \\ $$$$\left.\mathrm{2}\right)\:{give}\:{A}_{\mathrm{1}} \:{at}\:{form}\:{of}\:{serie}\:. \\ $$ Commented…