Question Number 29975 by abdo imad last updated on 14/Feb/18 $$\:{let}\:{give}\:\mathrm{0}<\alpha<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\pi\:{coth}\left(\pi\alpha\right)\:−\frac{\mathrm{1}}{\alpha}\:=\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\mathrm{2}\alpha}{\alpha^{\mathrm{2}} \:+{n}^{\mathrm{2}} }. \\ $$$$\left.\mathrm{2}\right){by}\:{integration}\:{on}\left[\mathrm{0},\mathrm{1}\right]\:{find}\:\prod_{{n}=\mathrm{1}} ^{\infty} \:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right). \\ $$ Commented…
Question Number 29976 by abdo imad last updated on 14/Feb/18 $${prove}\:{that} \\ $$$${ln}\left(\Gamma\left({x}\right)\right)=\:−{lnx}\:−\gamma{x}\:\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\left(\:\:\frac{{x}}{{n}}\:\:−{ln}\left(\:\mathrm{1}+\frac{{x}}{{n}}\right)\right)\:{with}\:{x}>\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 29971 by abdo imad last updated on 14/Feb/18 $${find}\:{J}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{{x}+{e}^{{t}} }\:\:\:\:?. \\ $$ Commented by abdo imad last updated on 16/Feb/18 $${J}\left({x}\right)=\:\int_{\mathrm{0}}…
Question Number 29972 by abdo imad last updated on 14/Feb/18 $${let}\:{give}\:\mid{x}\mid<\mathrm{1}\:{find}\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{d}\theta}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} {cos}^{\mathrm{2}} \theta}}\:. \\ $$ Commented by abdo imad last updated on 18/Feb/18…
Question Number 95494 by Ar Brandon last updated on 25/May/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 29957 by 7980812906 last updated on 14/Feb/18 $$\int\mathrm{3}{x}\mathrm{d}{x} \\ $$ Answered by Joel578 last updated on 14/Feb/18 $$\int\:\mathrm{3}{x}\:{dx}\:=\:\frac{\mathrm{3}}{\mathrm{2}}{x}^{\mathrm{2}} \:+\:{C} \\ $$ Terms of…
Question Number 161003 by mnjuly1970 last updated on 10/Dec/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 95449 by bobhans last updated on 25/May/20 $$\int\int\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\mathrm{dxdy}\:=\: \\ $$$$\mathrm{where}\:\mathrm{D}\::\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:\leqslant\:\mathrm{100}\: \\ $$ Commented by mr W last updated on…
Question Number 160982 by mnjuly1970 last updated on 10/Dec/21 $$ \\ $$$$\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}\:\left(−{ln}\:\left({x}\right)\right)}{\mathrm{1}+{x}}\:{dx}\:\overset{?} {=}\frac{−\mathrm{1}}{\mathrm{2}}\:{ln}^{\:\mathrm{2}} \left(\mathrm{2}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 160979 by amin96 last updated on 10/Dec/21 $$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} \boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}−\mathrm{1}} \boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}}=???\:\:\: \\ $$$$\boldsymbol{\mathrm{n}}\geqslant\mathrm{1} \\ $$ Answered by qaz last updated on 10/Dec/21 $$\Omega=−\underset{\mathrm{k}=\mathrm{1}}…