Question Number 130432 by mnjuly1970 last updated on 25/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{calculate}\::: \\ $$$$\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} {xln}\left({x}\right){e}^{−{x}} {sin}\left({x}\right){dx}=? \\ $$$$\:\:\: \\ $$ Answered by Dwaipayan Shikari…
Question Number 130433 by mnjuly1970 last updated on 25/Jan/21 $$\:\:\:\:\:\:….{nice}\:\:\:{calculus}… \\ $$$$\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\Psi=\int_{\mathrm{0}} ^{\:\infty} {e}^{−{x}} {ln}\left({x}\right){cos}\left({x}\right){dx}\overset{?} {=}\frac{\mathrm{1}}{\mathrm{8}}\left(−\mathrm{4}\gamma−\pi−\mathrm{2}{ln}\left(\mathrm{2}\right)\right) \\ $$$$ \\ $$ Answered by Dwaipayan…
Question Number 64895 by mathmax by abdo last updated on 22/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 130431 by mnjuly1970 last updated on 25/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:{calculus}… \\ $$$$\:{please}\:\:{evaluate}\::: \\ $$$$\:\:\:\phi=\int_{\mathrm{0}} ^{\:\infty} {tanh}\left({x}\right).{e}^{−{sx}} {dx}=?? \\ $$$$\:\:\:\:\:\:\:\left(\:\:{s}>\mathrm{0}\:\:\:{and}\:\:\:{real}…\right) \\ $$ Answered by Dwaipayan Shikari…
Question Number 64894 by mathmax by abdo last updated on 22/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64893 by mathmax by abdo last updated on 22/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64892 by mathmax by abdo last updated on 22/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 130426 by Koyoooo last updated on 25/Jan/21 Answered by Olaf last updated on 25/Jan/21 $$\left(\mathrm{9}×\mathrm{9}×\mathrm{9}×\mathrm{9}\right)_{\mathrm{10}} \:=\:\mathrm{100}_{\mathrm{81}} \\ $$$$\mathrm{9}^{\mathrm{4}} \:\mathrm{en}\:\mathrm{base}\:\mathrm{10}\:\mathrm{egale}\:\mathrm{100}\:\mathrm{en}\:\mathrm{base}\:\mathrm{81} \\ $$ Answered by…
Question Number 130422 by john_santu last updated on 25/Jan/21 $$\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\left(\frac{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{sin}\:\mathrm{2}{x}^{\mathrm{5}} \right)}{\mathrm{tan}\:^{\mathrm{3}} \mathrm{3}{x}\:\left(\mathrm{5}^{{x}^{\mathrm{2}} } −\mathrm{1}\right)}\right)\:=? \\ $$ Answered by liberty last updated on 25/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 64887 by ajfour last updated on 22/Jul/19 Answered by mr W last updated on 22/Jul/19 $${let}\:\lambda=\frac{{a}}{{R}} \\ $$$$\mathrm{cos}\:\alpha=\frac{\left(\frac{{a}}{\mathrm{2}}\right)^{\mathrm{2}} +{R}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}×\frac{{a}}{\mathrm{2}}×{R}}=\frac{\mathrm{4}{R}^{\mathrm{2}} −\mathrm{3}{a}^{\mathrm{2}} }{\mathrm{4}{aR}}=\frac{\mathrm{4}−\mathrm{3}\lambda^{\mathrm{2}}…