Question Number 37886 by abdo mathsup 649 cc last updated on 19/Jun/18 $${finf}\:\:{f}\left(\alpha\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{e}^{−\alpha{x}} \right){dx}\:\:{with}\:\alpha\geqslant\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 37884 by prof Abdo imad last updated on 18/Jun/18 $${let}\:{I}\:\:=\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left[{x}\right]} \:{cos}^{\mathrm{2}} \left(\mathrm{2}\pi{x}\right){dx}\:{and}\: \\ $$$${J}\:=\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left[{x}\right]} \:{sin}^{\mathrm{2}} \left(\mathrm{2}\pi{x}\right)\:{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:+{J}\:{and}\:{I}\:−{J} \\…
Question Number 103397 by frc2crc last updated on 14/Jul/20 $${I}\left({n}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\:{x}}{\mathrm{cosh}^{{n}} {x}\:}{dx} \\ $$$${is}\:{there}\:{a}\:{simpler}\:{way}\:{to} \\ $$$${calculat}\:{those}\:{values} \\ $$ Answered by Aziztisffola last updated on…
Question Number 168894 by mnjuly1970 last updated on 20/Apr/22 Commented by mahdipoor last updated on 20/Apr/22 $$\int\frac{\mathrm{1}}{\mathrm{12}}\left(\frac{\mathrm{3}−{x}}{{x}^{\mathrm{2}} +{x}}+\frac{{x}−\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}}\right){dx}= \\ $$$$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +{x}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}\right)}=\int\frac{{d}\left({lnx}\right)}{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}\right)}= \\…
Question Number 168898 by mathlove last updated on 20/Apr/22 Answered by FelipeLz last updated on 21/Apr/22 $$\mathrm{2}^{{x}} \:=\:{u}\:\Rightarrow\:{du}\:=\:\mathrm{2}^{{x}} \mathrm{ln}\left(\mathrm{2}\right){dx} \\ $$$$\int\mathrm{2}^{\mathrm{2}^{\mathrm{2}^{{x}} } } \mathrm{2}^{\mathrm{2}^{{x}} }…
Question Number 37820 by prof Abdo imad last updated on 17/Jun/18 $${let}\:{f}\left({x}\right)=\:\frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 37815 by prof Abdo imad last updated on 17/Jun/18 $${let}\:{I}\:\:=\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}} \:{cos}^{\mathrm{2}} \left(\pi\left[{x}\right]\right){dx}\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}} \:{sin}^{\mathrm{2}} \left(\pi\left[{x}\right]\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:+{J}\:\:{and}\:{I}\:−{J} \\…
Question Number 37812 by prof Abdo imad last updated on 17/Jun/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\mathrm{2}{x}} {sin}\left\{\pi\left[{x}\right]\right\}{dx}\:. \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 37813 by prof Abdo imad last updated on 17/Jun/18 $${find}\:{A}_{{n}} \:\:=\:\int_{\frac{\mathrm{1}}{{n}}} ^{\mathrm{1}} \:\:{x}\sqrt{{x}}{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right){dx} \\ $$$${then}\:{calculate}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} . \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 103343 by Dwaipayan Shikari last updated on 14/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{−{x}} {dx} \\ $$ Answered by mathmax by abdo last updated on 15/Jul/20…