Question Number 38209 by prof Abdo imad last updated on 22/Jun/18 $${let}\:{f}\left({x}\right)={e}^{−{x}} {cosx} \\ $$$${developp}\:{f}\:{at}\:{fourier}\:{serie} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=−\infty} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{1}+{n}^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}}…
Question Number 38207 by prof Abdo imad last updated on 22/Jun/18 $${prove}\:{that}\:{coth}\left({x}\right)−\frac{\mathrm{1}}{{x}}\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{2}{x}}{{x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} \pi^{\mathrm{2}} } \\ $$$$\left({x}\neq\mathrm{0}\right) \\ $$ Commented by math khazana…
Question Number 103742 by mathmax by abdo last updated on 17/Jul/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{\mathrm{dx}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{4}} \left(\mathrm{x}+\mathrm{3}\right)^{\mathrm{5}} } \\ $$ Answered by mathmax by abdo last updated…
Question Number 38205 by prof Abdo imad last updated on 22/Jun/18 $${if}\:\:\frac{\mathrm{1}}{{sinx}}\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:{a}_{{n}} {sin}\left({nx}\right)\:\:{find}\:{the}\:{values}\:{of} \\ $$$${a}_{{n}} . \\ $$ Terms of Service Privacy Policy…
Question Number 38204 by prof Abdo imad last updated on 22/Jun/18 $${if}\:\:\frac{\mathrm{1}}{{cosx}}\:=\frac{{a}_{\mathrm{0}} }{\mathrm{2}}\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:{a}_{{n}} {cos}\left({nx}\right) \\ $$$${calculate}\:{a}_{\mathrm{0}} \:{and}\:{a}_{{n}} \\ $$ Commented by math khazana…
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}\:}…