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}… \\ $$…
Question Number 128262 by Ahmed1hamouda last updated on 06/Jan/21 Answered by mr W last updated on 06/Jan/21 $$\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 128251 by rs4089 last updated on 05/Jan/21 Answered by mathmax by abdo last updated on 05/Jan/21 $$\mathrm{let}\:\mathrm{I}\:=\int_{−\infty} ^{+\infty} \:\mathrm{x}^{\mathrm{2}} \:\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} \:} \mathrm{cosx}\:\mathrm{dx}\:\Rightarrow\mathrm{I}\:=\int_{−\infty} ^{+\infty}…
Question Number 128244 by mnjuly1970 last updated on 05/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:\:::\Omega=\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({sin}\left({x}\right)\right){d}=\frac{−\pi}{\mathrm{4}}{log}\left(\mathrm{2}\right)−\frac{{G}}{\mathrm{2}} \\ $$$$\:\:\:\:{log}\left(\mathrm{2}{sin}\left({x}\right)\right)=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{−\mathrm{1}}{{n}}{cos}\left(\mathrm{2}{nx}\right) \\ $$$$\:\Omega=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \left\{−{log}\left(\mathrm{2}\right)−\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left(\mathrm{2}{nx}\right)}{{n}}\right\}{dx} \\…
Question Number 128221 by john_santu last updated on 05/Jan/21 $$\:{Given}\:{f}\left({x}+\frac{\mathrm{1}}{{x}}\right)\:=\:{x}^{\mathrm{4}} −\frac{\mathrm{1}}{{x}^{\mathrm{4}} }+\mathrm{2} \\ $$$$\:{then}\:\int_{\mathrm{1}} ^{\:\mathrm{2}} \left(\mathrm{1}−{x}^{−\mathrm{2}} \right){f}\left({x}\right){dx}= \\ $$ Answered by liberty last updated on…
Question Number 128194 by Algoritm last updated on 05/Jan/21 Commented by MJS_new last updated on 05/Jan/21 $$\mathrm{it}'\mathrm{s}\:\mathrm{possible}\:\mathrm{by}\:\mathrm{using} \\ $$$$\mathrm{cos}\:{x}\:=\frac{\mathrm{e}^{\mathrm{i}{x}} +\mathrm{e}^{−\mathrm{i}{x}} }{\mathrm{2}}=\frac{\mathrm{e}^{\mathrm{2i}{x}} +\mathrm{1}}{\mathrm{2e}^{\mathrm{i}{x}} }\:\Rightarrow \\ $$$$\mathrm{8}\int\frac{{x}\mathrm{e}^{\mathrm{3i}{x}}…
Question Number 128192 by Algoritm last updated on 05/Jan/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 62653 by aliesam last updated on 23/Jun/19 $$\int\mathrm{x}\left(\mathrm{arctan}\left(\mathrm{x}\right)\right)^{\mathrm{2}} \:\mathrm{dx} \\ $$$$ \\ $$$$\int\frac{\mathrm{x}\:\mathrm{e}^{\mathrm{arctan}\left(\mathrm{x}\right)} }{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:\mathrm{dx} \\ $$$$ \\ $$$$\int\frac{\mathrm{arcsin}\left(\mathrm{x}\right)}{\:\sqrt{\mathrm{1}+\mathrm{x}}}\:\mathrm{dx} \\ $$ Commented…
Question Number 62648 by Tawa1 last updated on 23/Jun/19 Commented by Tawa1 last updated on 23/Jun/19 $$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{integrate}\:\mathrm{the}\:\mathrm{integral}.\:\mathrm{Thanks} \\ $$ Terms of Service Privacy Policy Contact:…