Question Number 103741 by mathmax by abdo last updated on 17/Jul/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{arctan}\left(\mathrm{ch}\left(\mathrm{x}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{9}}\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 38203 by prof Abdo imad last updated on 22/Jun/18 $${let}\:{x}\neq\frac{\pi}{\mathrm{2}}+{k}\pi,{k}\in{Z}.{prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}{cosx}}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} \left({cos}\left(\mathrm{2}{n}+\mathrm{1}\right){x}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 38202 by prof Abdo imad last updated on 22/Jun/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{x}} \sqrt{\mathrm{1}−{e}^{−\mathrm{2}{x}} }{dx} \\ $$ Commented by math khazana by abdo last…
Question Number 169268 by amin96 last updated on 27/Apr/22 $$\boldsymbol{\Omega}=\int\frac{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)\right)}{\boldsymbol{\mathrm{tan}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}\boldsymbol{\mathrm{dx}}=? \\ $$ Answered by Mathspace last updated on 28/Apr/22 $${ln}\left({tan}\left(\frac{{x}}{\mathrm{2}}\right)\right)={t}\:\Rightarrow{tan}\left(\frac{{x}}{\mathrm{2}}\right)={e}^{{t}} \\ $$$$\Rightarrow{x}=\mathrm{2}{arctan}\left({e}^{{t}} \right)\:\Rightarrow \\…
Question Number 38199 by prof Abdo imad last updated on 22/Jun/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{\sqrt{{x}}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 24/Jun/18 $${x}={t}^{\mathrm{2}\:}…
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}}…