Question Number 137876 by Bekzod Jumayev last updated on 07/Apr/21 Answered by MJS_new last updated on 07/Apr/21 $$\int\frac{{dx}}{\left({x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{1}/\mathrm{3}} }= \\ $$$$\:\:\:\:\:\left[{t}=\frac{{x}}{\left({x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{1}/\mathrm{3}} }\:\rightarrow\:{dx}=−\left({x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{4}/\mathrm{3}}…
Question Number 137873 by mnjuly1970 last updated on 07/Apr/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:…….{nice}\:\:…………{calculus}……. \\ $$$$\:\:\:\:\boldsymbol{\phi}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({nx}\right)}{{n}}\:=\frac{\pi}{\mathrm{2}}−\frac{{x}}{\mathrm{2}} \\ $$$$\:\:\:\boldsymbol{\phi}=−{Im}\left(\mathrm{1}−{e}^{{ix}} \right)=−{Imln}\left\{\left(\mathrm{1}−{cos}\left({x}\right)−{isin}\left({x}\right)\right)\right\} \\ $$$$\:\:\:\:=−{Im}\left\{{ln}\left(\sqrt{\left(\mathrm{1}−{cos}\left({x}\right)\right)^{\mathrm{2}} +{sin}^{\mathrm{2}} \left({x}\right)}\:+{itan}^{−\mathrm{1}} \left(\frac{−{sin}\left({x}\right)}{\mathrm{1}−{cos}\left({x}\right)}\right)\right\}\right. \\…
Question Number 137874 by mnjuly1970 last updated on 07/Apr/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:…….{nice}\:…\:….\:{calculus}…. \\ $$$$\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{ln}\left(\mathrm{1}−{x}\right)}{{x}}\right)^{\mathrm{3}} =?…. \\ $$ Answered by EnterUsername last…
Question Number 72336 by Rio Michael last updated on 27/Oct/19 $${Obain}\:{an}\:{equation}\:{for}\: \\ $$$$\Rightarrow\:{the}\:{left}\:{Reimen}\:{Sum} \\ $$$$\Rightarrow\:{the}\:{right}\:{Reimen}\:{sum} \\ $$$$\Rightarrow\:{Trapeziodal}\:{rule} \\ $$$$\Rightarrow\:{Newton}\:{Raphson}'{s}\:{Iteration} \\ $$$$\:\:{Hence}\:{find}\:{and}\:{approximate}\:{value}\:{for}\:\int_{\mathrm{0}} ^{\mathrm{3}} \left({e}^{{x}} \:+\:{x}^{\mathrm{2}} \right){dx}…
Question Number 72337 by Rio Michael last updated on 27/Oct/19 $${Evaluate}\:\:\int_{−\mathrm{5}} ^{\mathrm{5}} \left(\sqrt{\mathrm{25}−{x}^{\mathrm{2}} }\:\right)\:{dx}\:{using} \\ $$$$\Rightarrow\:{an}\:{algebraic}\:{method} \\ $$$$\Rightarrow\:{Geometrical}\:{mehod}\: \\ $$$${thanks}\:{in}\:{advanced}\:{great}\:{mathematicians} \\ $$ Commented by mathmax…
Question Number 6790 by Yozzii last updated on 26/Jul/16 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\int_{{y}} ^{\mathrm{1}} \:{x}^{−\mathrm{3}/\mathrm{2}} {cos}\frac{\pi{y}}{\mathrm{2}{x}}\:{dx}\:{dy}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137838 by Bekzod Jumayev last updated on 07/Apr/21 $$\int{log}_{{x}} {edx}=?? \\ $$ Commented by mr W last updated on 07/Apr/21 $$=\int\frac{\mathrm{1}}{\mathrm{ln}\:{x}}{dx} \\ $$$$={li}\left({x}\right)+{C}…
Question Number 137829 by mnjuly1970 last updated on 07/Apr/21 $$\:\:\:\:\:…….{nice}\:\:…\:…\:….\:{calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:{that}\::::: \\ $$$$\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{log}\left(\mathrm{1}−{x}\right)}{{x}}\right)^{\mathrm{2}} {dx}=\mathrm{2}\zeta\left(\mathrm{2}\right)…. \\ $$$$ \\ $$ Answered by EnterUsername last…
Question Number 72286 by Best last updated on 27/Oct/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 6748 by Leila Akram last updated on 21/Jul/16 Answered by Yozzii last updated on 21/Jul/16 $${I}=\int_{−\mathrm{1}} ^{\mathrm{0}} {t}\sqrt{{t}+\mathrm{2}}{dx} \\ $$$${u}={t}+\mathrm{2}\Rightarrow{du}={dt} \\ $$$${t}={u}−\mathrm{2} \\…