Question Number 62335 by maxmathsup by imad last updated on 19/Jun/19 $$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−{xt}} {cos}\left({yt}\right)}{\:\sqrt{{t}}}\:{dt}\:{and}\:{g}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{xt}} {sin}\left({yt}\right)}{\:\sqrt{{t}}}\:{dt} \\ $$$${with}\:{x}>\mathrm{0}\:\:{and}\:{y}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{−\mathrm{2}{t}} \:{cos}\left({t}\right)}{\:\sqrt{{t}}}\:{dt}\:{and}\:\int_{\mathrm{0}}…
Question Number 62330 by maxmathsup by imad last updated on 19/Jun/19 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{a}−\mathrm{1}} }{\left(\mathrm{1}+{t}\right)^{\mathrm{2}} }{dt}\:\:\:{with}\:\:\:\mathrm{0}<{a}<\mathrm{1} \\ $$ Commented by mathmax by abdo last updated…
Question Number 127857 by slahadjb last updated on 02/Jan/21 $$\int\sqrt{{x}}{e}^{{x}} {dx}\:\:? \\ $$ Commented by Dwaipayan Shikari last updated on 02/Jan/21 $$\int{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{{n}}…
Question Number 127851 by bemath last updated on 02/Jan/21 $$\:\psi\:=\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} \:\sqrt[{\mathrm{5}}]{\left(\mathrm{x}^{\mathrm{5}} +\mathrm{1}\right)^{\mathrm{3}} }}\:?\: \\ $$ Answered by liberty last updated on 02/Jan/21 $$\:\psi\:=\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} \:\sqrt[{\mathrm{5}}]{\mathrm{x}^{\mathrm{15}} \left(\mathrm{1}+\mathrm{x}^{−\mathrm{5}}…
Question Number 127833 by Algoritm last updated on 02/Jan/21 Answered by mathmax by abdo last updated on 02/Jan/21 $$\mathrm{I}\:=\int_{\mathrm{0}} ^{\mathrm{4}} \:\frac{\mathrm{cosx}}{\:\sqrt{\mathrm{4}−\mathrm{x}}}\mathrm{dx}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\sqrt{\mathrm{4}−\mathrm{x}}=\mathrm{t}\:\Rightarrow\mathrm{4}−\mathrm{x}=\mathrm{t}^{\mathrm{2}} \\ $$$$\mathrm{I}\:=\int_{\mathrm{2}} ^{\mathrm{0}} \:\frac{\mathrm{cos}\left(\mathrm{4}−\mathrm{t}^{\mathrm{2}}…
Question Number 127815 by Algoritm last updated on 02/Jan/21 Commented by Algoritm last updated on 02/Jan/21 $$\mathrm{prove}\:\mathrm{the}\:\mathrm{equation} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 62274 by aliesam last updated on 18/Jun/19 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}{e}^{−{x}^{\mathrm{2}} } \:{dx} \\ $$ Commented by maxmathsup by imad last updated on 19/Jun/19…
Question Number 62266 by aliesam last updated on 18/Jun/19 $$\int\frac{\mathrm{2}{sin}\left({x}\right)+\mathrm{3}{cos}\left({x}\right)}{\mathrm{3}{sin}\left({x}\right)+\mathrm{4}{cos}\left({x}\right)}{dx} \\ $$ Commented by maxmathsup by imad last updated on 19/Jun/19 $${let}\:{A}\:=\int\:\:\:\frac{\mathrm{2}{sinx}\:+\mathrm{3}{cosx}}{\mathrm{3}{sinx}\:+\mathrm{4}{cosx}}\:{dx}\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\ $$$${A}\:=\int\:\:\:\frac{\frac{\mathrm{4}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }+\mathrm{3}\frac{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 62262 by maxmathsup by imad last updated on 18/Jun/19 $${find}\:{the}\:{value}\:{of}\: \\ $$$${I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{t}} {sint}}{\:\sqrt{{t}}}{dt}\:\:{and}\:{J}\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{t}} {cos}\left({t}\right)}{\:\sqrt{{t}}}{dt}\:\:,{study}\:{first}\:{the}\:{convergence}. \\ $$ Commented by maxmathsup…
Question Number 127789 by AyaDouae last updated on 02/Jan/21 Commented by khaki last updated on 02/Jan/21 $$\mathrm{how}\:\mathrm{cn}\:\mathrm{i}\:\mathrm{upload}\:\mathrm{my}\:\mathrm{qudstion}\:\mathrm{please}\:\mathrm{help}\:\mathrm{me} \\ $$ Commented by mr W last updated…