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Question Number 163490 by Zaynal last updated on 07/Jan/22 $$\int_{\mathrm{0}} ^{\infty} \:\frac{\boldsymbol{{x}}^{\mathrm{3}} }{\boldsymbol{{e}}^{\boldsymbol{{x}}} \:−\mathrm{1}}\:\boldsymbol{{dx}} \\ $$ Answered by mnjuly1970 last updated on 07/Jan/22 $$\:\:\:\:\Gamma\:\left(\mathrm{4}\right).\zeta\:\left(\mathrm{4}\right)=\:\frac{\pi^{\:\mathrm{4}} }{\mathrm{15}}…
Question Number 163483 by Zaynal last updated on 07/Jan/22 Answered by alephzero last updated on 07/Jan/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{4}{x}^{\mathrm{3}} \left\{\frac{{d}^{\mathrm{2}} }{{dx}^{\mathrm{2}} }\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{5}} \right\}{dx}\:=\:? \\…
Question Number 163481 by smallEinstein last updated on 07/Jan/22 Answered by Mathspace last updated on 07/Jan/22 $$\Psi_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{{n}} \right){logx}\:{dx} \\ $$$${letf}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} {x}^{{a}}…
Question Number 163472 by Zaynal last updated on 07/Jan/22 $$\int_{\mathrm{0}} ^{\mathrm{3}} \:\frac{\boldsymbol{\mathrm{xdx}}}{\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:+\:\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:+\:\boldsymbol{\mathrm{x}}\:\mathrm{2}}\:= \\ $$ Answered by alephzero last updated on 07/Jan/22 $$\int_{\mathrm{0}} ^{\mathrm{3}}…
Question Number 163473 by Zaynal last updated on 07/Jan/22 Commented by riyaj last updated on 07/Jan/22 $$ \\ $$ Commented by Zaynal last updated on…
Question Number 163469 by Zaynal last updated on 07/Jan/22 Commented by smallEinstein last updated on 07/Jan/22 Answered by amin96 last updated on 07/Jan/22 $$\Omega=−\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 97928 by M±th+et+s last updated on 10/Jun/20 $${find}\:{the}\:{general}\:{formula} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {tan}^{\alpha} \left({x}\right)\:{dx} \\ $$ Answered by abdomathmax last updated on 10/Jun/20 $$\mathrm{I}\:=\int_{\mathrm{0}}…
Question Number 163467 by Zaynal last updated on 07/Jan/22 Answered by mr W last updated on 07/Jan/22 $${e}^{{x}} =\mathrm{1}+\frac{{x}}{\mathrm{1}!}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}!}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}!}…=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{\mathrm{2}{n}} }{\left(\mathrm{2}{n}\right)!}+\underset{{n}=\mathrm{0}} {\overset{\infty}…