Category: Integration

Question Number 119442 by mnjuly1970 last updated on 24/Oct/20 $$\dots advancedcalculus\dots$$$$provethat:\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{n^2\left(\begin{array}{c}2n\\ n\end{array}\right)}\stackrel{???}{=}\frac{\zeta \left(2\right)}{3}$$$${solution}::\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} \ast\frac{\left(\mathrm{2}{n}\right)!}{\left({n}!\right)^{\mathrm{2}} }}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}!\ast{n}!}{{n}^{\mathrm{2}} \ast\left(\mathrm{2}{n}\right)!}\:…

Question Number 119425 by mathmax by abdo last updated on 24/Oct/20 $$\mathrm{decompose}\mathrm{F}\left(\mathrm{x}\right)=\frac{2\mathrm{x}-1}{{({\mathrm{x}}^2-1)}^2({\mathrm{x}}^2+3)}$$$$\mathrm{and}\mathrm{calculate}{\int }_{\sqrt{2}}^{+\mathrm{\infty }}\mathrm{F}\left(\mathrm{x}\right)\mathrm{dx}$$ Answered by 1549442205PVT last…

Question Number 53843 by rahul 19 last updated on 26/Jan/19 Answered by tanmay.chaudhury50@gmail.com last updated on 26/Jan/19 $$\frac{{df}}{{dx}}=\int_{{x}^{\mathrm{2}} } ^{{x}^{\mathrm{3}} } \:\frac{\partial}{\partial{x}}\left(\frac{\mathrm{1}}{{lnt}}\right){dt}+\frac{\mathrm{1}}{{lnx}^{\mathrm{3}} }\frac{{d}\left({x}^{\mathrm{3}} \right)}{{dx}}−\frac{\mathrm{1}}{{lnx}^{\mathrm{2}} }\frac{{d}\left({x}^{\mathrm{2}}…

Question Number 119323 by mnjuly1970 last updated on 23/Oct/20 Commented by Dwaipayan Shikari last updated on 23/Oct/20 $$Whatis\eta (2n+1)?$$ Commented by mnjuly1970 last updated…

Question Number 53783 by maxmathsup by imad last updated on 25/Jan/19 $$calculate{\int }_0^{\mathrm{\infty }}\frac{t^2}{e^t-1}dtintermsof\xi \left(3\right)$$ Answered by Smail last updated on 26/Jan/19…