Question Number 197919 by universe last updated on 04/Oct/23 $$\:\:\:\:\:\:\mathrm{I}_{{m}} \:\:\:\:\:=\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\frac{\lfloor\mathrm{2}^{{m}} {x}\rfloor}{\mathrm{3}^{{m}} }\:\underset{{n}={m}+\mathrm{1}} {\overset{\infty} {\sum}}\frac{\lfloor\mathrm{2}^{{n}} {x}\rfloor}{\mathrm{3}^{{n}} }\right){dx} \\ $$$$\:\:\:\:\:\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\mathrm{I}\:=\:\:\:\underset{{m}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{I}_{{m}}…
Question Number 197906 by mnjuly1970 last updated on 03/Oct/23 $$ \\ $$$$\:\:\:\:\:\:\:\mathrm{S}=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\:\Gamma^{\:\mathrm{2}} \left(\:{k}\:\right)}{{k}\:\Gamma\:\left(\mathrm{2}{k}\:\right)}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:−−−− \\ $$ Answered by Dwan last updated on…
Question Number 197821 by mnjuly1970 last updated on 30/Sep/23 $$ \\ $$$$\:\:\:\:{find}\:{the}\:{value}\:\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\:\mathrm{ln}\:\left(\:\mathrm{1}+\:\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} }\:\right)}{\mathrm{2}\:+\:{x}^{\:\mathrm{2}} }\:{dx}\:=\:? \\ $$$$ \\ $$ Answered…
Question Number 197819 by mnjuly1970 last updated on 30/Sep/23 $$ \\ $$$$\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}\:\:: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:{H}_{\:\mathrm{2}{n}} }{{n}}\:=\:? \\ $$$${where},{H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}}\:+…+\frac{\mathrm{1}}{{n}} \\ $$ Answered by…
Question Number 197802 by cortano12 last updated on 29/Sep/23 $$\:\:\:\mathrm{I}=\underset{−\mathrm{2}} {\overset{\mathrm{6}} {\int}}\:\frac{\mid\mathrm{x}−\mathrm{1}\mid}{\mathrm{x}−\mathrm{1}}\:\mathrm{dx}\:=? \\ $$ Answered by MM42 last updated on 29/Sep/23 $${I}=\int_{−\mathrm{2}} ^{\mathrm{1}} −{dx}+\int_{\mathrm{1}} ^{\mathrm{6}}…
Question Number 197783 by pticantor last updated on 28/Sep/23 $$\int\frac{{x}.\boldsymbol{{arctg}}\left(\boldsymbol{{x}}\right)}{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}\boldsymbol{{dx}}=? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$ Answered by EmGent last…
Question Number 197767 by AR19 last updated on 28/Sep/23 Commented by Frix last updated on 28/Sep/23 $$\int\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}{dx}={x}\:_{\mathrm{2}} {F}_{\mathrm{1}} \:\left(−\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{1}}{\mathrm{3}};\:\frac{\mathrm{4}}{\mathrm{3}};\:−{x}^{\mathrm{3}} \right)\:+{C} \\ $$ Terms of…
Question Number 197734 by pticantor last updated on 27/Sep/23 $$\boldsymbol{{c}}{alcul}\:\int\left(\boldsymbol{{lnx}}\right)^{\sqrt{\boldsymbol{{x}}}} \boldsymbol{{dx}} \\ $$$$\boldsymbol{{help}}\:\:\boldsymbol{{pls}} \\ $$ Answered by Frix last updated on 27/Sep/23 $$\mathrm{Impossible}. \\ $$…
Question Number 197744 by mathlove last updated on 27/Sep/23 $$\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} {x}\:{dx}=? \\ $$ Answered by witcher3 last updated on 27/Sep/23 $$\int\mathrm{2tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\mathrm{dx}=\mathrm{2xtan}^{−\mathrm{1}} \left(\mathrm{x}\right)−\int\frac{\mathrm{2x}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}}…
Question Number 197659 by pticantor last updated on 25/Sep/23 Terms of Service Privacy Policy Contact: info@tinkutara.com