Question Number 119445 by mnjuly1970 last updated on 24/Oct/20 $$\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\mathrm{3}} \begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}}\:\overset{???} {=}\zeta\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$ Terms of…
Question Number 119425 by mathmax by abdo last updated on 24/Oct/20 $$\mathrm{decompose}\:\mathrm{F}\left(\mathrm{x}\right)\:=\frac{\mathrm{2x}−\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} +\mathrm{3}\right)} \\ $$$$\mathrm{and}\:\mathrm{calculate}\:\int_{\sqrt{\mathrm{2}}} ^{+\infty} \mathrm{F}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by 1549442205PVT last…
Question Number 184925 by cortano1 last updated on 14/Jan/23 Commented by Frix last updated on 14/Jan/23 $$\mathrm{I}\:\mathrm{think}\:\mathrm{that} \\ $$$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{\mathrm{tan}^{−\mathrm{1}} \:{ax}\:−\mathrm{tan}^{−\mathrm{1}} \:{bx}}{{x}}{dx}=\frac{\pi}{\mathrm{2}}\mathrm{ln}\:\frac{{a}}{{b}} \\ $$…
Question Number 53843 by rahul 19 last updated on 26/Jan/19 Answered by tanmay.chaudhury50@gmail.com last updated on 26/Jan/19 $$\frac{{df}}{{dx}}=\int_{{x}^{\mathrm{2}} } ^{{x}^{\mathrm{3}} } \:\frac{\partial}{\partial{x}}\left(\frac{\mathrm{1}}{{lnt}}\right){dt}+\frac{\mathrm{1}}{{lnx}^{\mathrm{3}} }\frac{{d}\left({x}^{\mathrm{3}} \right)}{{dx}}−\frac{\mathrm{1}}{{lnx}^{\mathrm{2}} }\frac{{d}\left({x}^{\mathrm{2}}…
Question Number 119335 by physicstutes last updated on 23/Oct/20 $$\:\mathrm{Express}\:{f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)}\:\:\mathrm{into}\:\mathrm{partial}\:\mathrm{fractions}. \\ $$$$\mathrm{hence}\:\mathrm{evaluate}\:{I}\:=\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:{f}\left({x}\right)\:{dx} \\ $$ Answered by floor(10²Eta[1]) last updated on 23/Oct/20…
Question Number 119323 by mnjuly1970 last updated on 23/Oct/20 Commented by Dwaipayan Shikari last updated on 23/Oct/20 $${What}\:{is}\:\eta\left(\mathrm{2}{n}+\mathrm{1}\right)? \\ $$ Commented by mnjuly1970 last updated…
Question Number 53785 by maxmathsup by imad last updated on 25/Jan/19 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\frac{{tsin}\left({tx}\right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{tsin}\left(\mathrm{2}{t}\right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt}. \\ $$ Commented…
Question Number 53783 by maxmathsup by imad last updated on 25/Jan/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{t}^{\mathrm{2}} }{{e}^{{t}} −\mathrm{1}}{dt}\:{interms}\:{of}\:\xi\left(\mathrm{3}\right) \\ $$ Answered by Smail last updated on 26/Jan/19…
Question Number 119318 by Bird last updated on 23/Oct/20 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{lnx}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{2}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 53782 by maxmathsup by imad last updated on 25/Jan/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{3}} }{dt} \\ $$ Answered by Smail last updated on 26/Jan/19…