Question Number 128334 by liberty last updated on 06/Jan/21 $$\Omega\:=\:\int\:\frac{\mathrm{x}^{\mathrm{2}} }{\:\sqrt{\left(\mathrm{a}+\mathrm{bx}^{\mathrm{2}} \right)^{\mathrm{5}} }}\:\mathrm{dx}\:;\:\mathrm{where}\::\:\mathrm{a};\:\mathrm{b}\:>\mathrm{0}\: \\ $$ Answered by bramlexs22 last updated on 06/Jan/21 $$\Omega\:=\:\int\:\frac{{x}^{\mathrm{2}} }{\left({a}+{bx}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}}…
Question Number 62790 by Tawa1 last updated on 25/Jun/19 Commented by Tawa1 last updated on 25/Jun/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral} \\ $$ Answered by MJS last updated on…
Question Number 128316 by mnjuly1970 last updated on 08/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:{nice}\:\:{calculus} \\ $$$$\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx}=? \\ $$$$ \\ $$ Answered by mindispower last updated…
Question Number 62781 by Tawa1 last updated on 25/Jun/19 $$\int\:\mathrm{sec}\left(\mathrm{2x}\right)\:\mathrm{e}^{\mathrm{2x}} \:\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128285 by john_santu last updated on 06/Jan/21 $$\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{7}}\right)−\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:=? \\ $$ Answered by liberty last updated on 06/Jan/21 $$\:\mathrm{let}\:\varphi\:=\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{7}}\right)−\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right) \\ $$$$\:\varphi\:=\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{7}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{5}\pi}{\mathrm{7}}\right) \\ $$$$\:\Rightarrow\mathrm{2}\varphi\mathrm{sin}\:\mathrm{t}\:=\:\mathrm{2sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{t}\:+\:\mathrm{2sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{3t}+\mathrm{2sin}\:\mathrm{tcos}\:\mathrm{5t} \\…
Question Number 128276 by john_santu last updated on 06/Jan/21 $$\:\int_{{e}^{\mathrm{2}} } ^{\:\infty} \:\frac{{dx}}{{x}^{\mathrm{3}} \:\mathrm{ln}\:{x}}\:? \\ $$ Answered by liberty last updated on 06/Jan/21 $$\:\digamma\:=\:\underset{\mathrm{Y}\rightarrow+\infty} {\mathrm{lim}}\int_{\mathrm{e}^{\mathrm{2}}…
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}…