Question Number 53950 by maxmathsup by imad last updated on 27/Jan/19 $$\:{calculate}\:\int_{\frac{\mathrm{1}}{\mathrm{3}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\:\Gamma\left({x}\right)\Gamma\left(\mathrm{1}−{x}\right){dx}\:\:\:{with}\:\Gamma\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} {dt}\:\:\:\:{with}\:{x}>\mathrm{0}\:. \\ $$ Commented by maxmathsup by imad…
Question Number 53931 by zambolly19 last updated on 27/Jan/19 $$\int{x}!{dx} \\ $$ Commented by maxmathsup by imad last updated on 31/Jan/19 $${sir}\:{define}\:{first}\:{x}!….. \\ $$ Terms…
Question Number 119462 by mnjuly1970 last updated on 24/Oct/20 $$\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:{calculus}… \\ $$$$\:\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \:\frac{{tan}^{−\mathrm{1}} \left({x}\right)}{{e}^{\mathrm{2}\pi{x}} −\mathrm{1}}{dx}\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$ Answered by mathmax…
Question Number 184988 by saboorhalimi last updated on 15/Jan/23 Answered by a.lgnaoui last updated on 15/Jan/23 $$\Omega=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left({k}\mathrm{cos}\:\left({nx}\right)+{m}\mathrm{sin}\:{nx}\right){dx}+ \\ $$$$\int_{\frac{\pi}{\mathrm{2}}} ^{\pi} \left({k}\mathrm{cos}\:\left({nx}\right)+{m}\mathrm{sin}\:{nx}\right){dx} \\ $$$$=\left[\frac{{k}}{{n}}\mathrm{sin}\:{nx}−\frac{{m}}{{n}}\mathrm{cos}\:{nx}\right]_{\mathrm{0}}…
Question Number 119446 by Bird last updated on 24/Oct/20 $${calculste}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{3}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 119442 by mnjuly1970 last updated on 24/Oct/20 $$\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\::\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} \begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}}\:\overset{???} {=}\frac{\zeta\left(\mathrm{2}\right)}{\mathrm{3}} \\ $$$${solution}::\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{\mathrm{2}} \ast\frac{\left(\mathrm{2}{n}\right)!}{\left({n}!\right)^{\mathrm{2}} }}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}!\ast{n}!}{{n}^{\mathrm{2}} \ast\left(\mathrm{2}{n}\right)!}\:…
Question Number 119445 by mnjuly1970 last updated on 24/Oct/20 $$\:\:\:\:\:\:\:\:\:\:…{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}}…