Question Number 129936 by liberty last updated on 21/Jan/21 $$\:\mathrm{Nice}\:\mathrm{integral}\: \\ $$$$ \\ $$$$\:\:\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{sin}\:\left({x}\right)\:\mathrm{ln}\:\left({x}\right)\:\mathrm{e}^{−{x}} \:{dx}\: \\ $$ Answered by Lordose last updated on…
Question Number 129926 by mnjuly1970 last updated on 20/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}… \\ $$$$\:\:{evaluate}: \\ $$$$\:\:\:\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{{m}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\left({k}+{m}+{n}\right)!}\right)=? \\ $$$$ \\ $$ Answered…
Question Number 64392 by mathmax by abdo last updated on 17/Jul/19 $$\left.\mathrm{1}\right){calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left({x}^{\mathrm{2}{n}} \right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergene}\:{of}\:\Sigma\:{A}_{{n}} \\ $$ Commented by mathmax…
Question Number 64390 by mathmax by abdo last updated on 17/Jul/19 $${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{dx}}{{x}\sqrt{\mathrm{4}+{x}^{\mathrm{2}} }} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 129921 by stelor last updated on 20/Jan/21 $$\int\frac{\mathrm{1}}{\left(\mathrm{1}−\mathrm{u}^{\mathrm{2}} \right)^{\mathrm{2}} \mathrm{u}^{\mathrm{5}} }\mathrm{du}=?? \\ $$$$\mathrm{please}… \\ $$ Answered by Ar Brandon last updated on 20/Jan/21…
Question Number 64382 by Chi Mes Try last updated on 17/Jul/19 $${please}\:\:{help}\:{with}\:{workings} \\ $$$$ \\ $$$$\int{Ln}\left[\sqrt{}\left(\mathrm{1}−{x}\right)+\sqrt{}\left(\mathrm{1}+{x}\right)\right]{dx} \\ $$ Answered by MJS last updated on 17/Jul/19…
Question Number 129907 by pticantor last updated on 20/Jan/21 $$\int\frac{\boldsymbol{{dx}}}{\boldsymbol{{sin}}^{\mathrm{3}} \boldsymbol{{xcos}}^{\mathrm{5}} \boldsymbol{{x}}}=??????? \\ $$ Answered by Ar Brandon last updated on 20/Jan/21 $$\mathcal{I}=\int\frac{\mathrm{dx}}{\mathrm{sin}^{\mathrm{3}} \mathrm{xcos}^{\mathrm{5}} \mathrm{x}}=\int\frac{\mathrm{cos}^{\mathrm{2}}…
Question Number 129868 by Bird last updated on 20/Jan/21 $${find}\:{lim}_{{n}\rightarrow+\infty} \frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\frac{{k}}{\:\sqrt{\mathrm{4}{n}^{\mathrm{2}} −{k}^{\mathrm{2}} }} \\ $$ Answered by Ar Brandon last updated on 20/Jan/21…
Question Number 129867 by Bird last updated on 20/Jan/21 $${calculate}\:\int\:\:\:\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$ Answered by Olaf last updated on 20/Jan/21 $$\Omega\:=\:\int\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}\:=\:\int\frac{{du}}{{u}^{\mathrm{3}} }…
Question Number 129859 by EDWIN88 last updated on 20/Jan/21 $$\:\mathrm{L}\:=\:\int_{−\mathrm{1}} ^{\:\mathrm{0}} \sqrt{\frac{\mathrm{1}+\mathrm{y}}{\mathrm{1}−\mathrm{y}}}\:\mathrm{dy}\: \\ $$ Answered by liberty last updated on 20/Jan/21 $$\:\mathrm{let}\:\mathrm{y}=\mathrm{cos}\:\mathrm{2t}\:\rightarrow\begin{cases}{\mathrm{y}=\mathrm{0}\rightarrow\mathrm{t}=\frac{\pi}{\mathrm{4}}}\\{\mathrm{y}=−\mathrm{1}\rightarrow\mathrm{t}=\frac{\pi}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{L}\:=\int_{\pi/\mathrm{2}} ^{\:\pi/\mathrm{4}}…