Question Number 62732 by mathmax by abdo last updated on 24/Jun/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}{cosx}\:−{sin}\left({x}\right)}{dx}\: \\ $$ Answered by MJS last updated on 24/Jun/19 $$\frac{\mathrm{cos}\:\left(\mathrm{2}\left({x}+\pi\right)\right)}{\mathrm{2cos}\:\left({x}+\pi\right)\:−\mathrm{sin}\:\left({x}+\pi\right)}=−\frac{\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{2cos}\:{x}\:−\mathrm{sin}\:{x}}\:\Rightarrow \\…
Question Number 62731 by mathmax by abdo last updated on 24/Jun/19 $${find}\:\int\:\sqrt{\frac{{x}−\mathrm{1}}{{x}^{\mathrm{2}} \:+\mathrm{3}}}{dx}\: \\ $$ Commented by MJS last updated on 24/Jun/19 $$…\mathrm{seems}\:\mathrm{impossible}… \\ $$…
Question Number 128264 by bobhans last updated on 06/Jan/21 $$\sqrt[{\mathrm{8}\:\:\:\:}]{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−…}}}}} \\ $$ Commented by MJS_new last updated on 06/Jan/21 $$\frac{\mathrm{3}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$ Commented by bobhans…
Question Number 128262 by Ahmed1hamouda last updated on 06/Jan/21 Answered by mr W last updated on 06/Jan/21 $$\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{dxdy}}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 128256 by Dwaipayan Shikari last updated on 05/Jan/21 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}!\mathrm{1}!}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{3}!\mathrm{2}!}\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{4}!\mathrm{3}!}\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} }\right)^{\mathrm{2}} +….=\frac{\mathrm{4}}{\pi} \\ $$$${Prove}\:{the}\:{above}\:{Relation} \\ $$ Commented by Dwaipayan Shikari last…
Question Number 128254 by Ahmed1hamouda last updated on 05/Jan/21 Answered by mr W last updated on 06/Jan/21 $$\frac{{dy}}{{dx}}+\mathrm{2}{xy}={xe}^{−{x}} \\ $$$${IF}={e}^{\int\mathrm{2}{xdx}} ={e}^{{x}^{\mathrm{2}} } \\ $$$${y}=\frac{\int{e}^{{x}^{\mathrm{2}} }…
Question Number 128251 by rs4089 last updated on 05/Jan/21 Answered by mathmax by abdo last updated on 05/Jan/21 $$\mathrm{let}\:\mathrm{I}\:=\int_{−\infty} ^{+\infty} \:\mathrm{x}^{\mathrm{2}} \:\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} \:} \mathrm{cosx}\:\mathrm{dx}\:\Rightarrow\mathrm{I}\:=\int_{−\infty} ^{+\infty}…
Question Number 62712 by 30043018 last updated on 24/Jun/19 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128246 by mnjuly1970 last updated on 05/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:{suppose}\:{that}\:\:::\:{m}=\frac{\mathrm{4}^{{p}} −\mathrm{1}}{\mathrm{3}}\:,\:\:{where} \\ $$$$\:\:\:\:\:\:\:{p}\:\:{is}\:\:{a}\:{prime}\:{number}\:{and}\:\:{p}>\mathrm{3}. \\ $$$${prove}\:\:{that}\:\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}^{{m}−\mathrm{1}} \:\overset{{m}} {\equiv}\:\mathrm{1}\:\:\:\:…? \\ $$$$\: \\ $$…
Question Number 128244 by mnjuly1970 last updated on 05/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:\:::\Omega=\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({sin}\left({x}\right)\right){d}=\frac{−\pi}{\mathrm{4}}{log}\left(\mathrm{2}\right)−\frac{{G}}{\mathrm{2}} \\ $$$$\:\:\:\:{log}\left(\mathrm{2}{sin}\left({x}\right)\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{−\mathrm{1}}{{n}}{cos}\left(\mathrm{2}{nx}\right) \\ $$$$\:\Omega=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \left\{−{log}\left(\mathrm{2}\right)−\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left(\mathrm{2}{nx}\right)}{{n}}\right\}{dx} \\…