Question Number 38201 by prof Abdo imad last updated on 22/Jun/18 $${calculate}\:{I}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:{xe}^{−{x}^{\mathrm{2}} } \sqrt{\mathrm{1}−{e}^{−\mathrm{2}{x}^{\mathrm{2}} } }{dx} \\ $$ Terms of Service Privacy Policy…
Question Number 38198 by maxmathsup by imad last updated on 22/Jun/18 $${we}\:{give}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{x}} {ln}\left({x}\right){dx}=−\gamma \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{f}\left({a}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{ax}} {ln}\left({x}\right){dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{u}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{nx}}…
Question Number 38197 by maxmathsup by imad last updated on 22/Jun/18 $${find}\:{a}\:{simple}\:{form}\:{of}\:{L}\left({e}^{−\sqrt{{x}}} \right)\:\:{L}\:{is}\:{laplace}\:{transform} \\ $$ Commented by math khazana by abdo last updated on 25/Jun/18…
Question Number 103721 by Dwaipayan Shikari last updated on 16/Jul/20 $$\int_{\mathrm{0}} ^{\infty} \frac{{cosx}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$ Answered by Ar Brandon last updated on 16/Jul/20 $$\mathcal{I}=\int_{\mathrm{0}}…
Question Number 169259 by mathlove last updated on 27/Apr/22 Commented by infinityaction last updated on 27/Apr/22 $$\:\:\:\:\:\:\:\:{I}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{ax}} }{{x}}\:{dx}\:\:\:\:\:\:{and}\:\:\:\:{I}\left({b}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{bx}} }{{x}}{dx} \\ $$$$\:\:\:\:\:\:{I}'\left({a}\right)\:\:=\:\:−\int_{\mathrm{0}}…
Question Number 103723 by Ar Brandon last updated on 16/Jul/20 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{n},\:\mathrm{such}\:\mathrm{that}; \\ $$$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\centerdot\centerdot\centerdot+\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}+\mathrm{1}}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{x}^{\mathrm{n}+\mathrm{1}} }{\mathrm{1}+\mathrm{x}}\mathrm{dx}−\mathrm{ln2}−\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 169253 by Mastermind last updated on 27/Apr/22 $$\int\frac{−{sinx}}{{e}^{{x}} }{dx} \\ $$$$ \\ $$$${Mastermind} \\ $$ Answered by thfchristopher last updated on 27/Apr/22 $$=-\int{e}^{-{x}}…
Question Number 169230 by Giantyusuf last updated on 26/Apr/22 Answered by Mathspace last updated on 26/Apr/22 $${I}=_{{x}=\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{4}}} {t}} \:\:\:\int\:\:\:\:\frac{\sqrt{\mathrm{3}}{t}^{\mathrm{2}} }{\mathrm{3}\left(\mathrm{1}+{t}^{\mathrm{4}} \right)}\mathrm{3}^{\frac{\mathrm{1}}{\mathrm{4}}} {dt} \\ $$$$=\mathrm{3}^{−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}} \:\int\:\:\frac{{t}^{\mathrm{2}}…
Question Number 103683 by Dwaipayan Shikari last updated on 16/Jul/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{1}+{x}−{x}^{\mathrm{2}} }\right){dx} \\ $$ Commented by Dwaipayan Shikari last updated on 16/Jul/20…
Question Number 38130 by gunawan last updated on 22/Jun/18 $$\mathrm{1}.\:\int\mathrm{tan}^{\mathrm{3}} \left(\mathrm{2}{x}\right)\mathrm{sec}^{\mathrm{5}} \left(\mathrm{2}{x}\right)\:{dx}\: \\ $$$$\mathrm{2}.\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \mathrm{tan}^{\mathrm{5}} \left({x}\right)\mathrm{sec}^{\mathrm{6}} \left({x}\right)\:{dx}\: \\ $$$$\mathrm{3}.\:\int\mathrm{tan}^{\mathrm{6}} \left({ay}\right)\:{dy}\: \\ $$ Answered by…