Question Number 150121 by mathdanisur last updated on 09/Aug/21 $$\mathrm{Find}\:\mathrm{in}\:\mathrm{closed}\:\mathrm{form}:\:\:\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{ln}\left(\mathrm{1}\:-\:\mathrm{x}^{\mathrm{2}} \right)\mathrm{ln}^{\boldsymbol{\mathrm{n}}} \left(\mathrm{1}\:-\:\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\ $$ Answered by Kamel last updated on 09/Aug/21…
Question Number 150119 by mathdanisur last updated on 09/Aug/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{given} \\ $$$$\mathrm{expression}: \\ $$$$\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{6x}\:+\:\mathrm{8}\right)^{\mathrm{2}} \:+\:\mathrm{5} \\ $$ Answered by Ar Brandon last updated on…
Question Number 150097 by mathdanisur last updated on 09/Aug/21 Answered by Kamel last updated on 09/Aug/21 $${u}_{{n}} =\underset{{p}=\mathrm{0}} {\overset{{m}} {\prod}}\gamma_{{n}+{p}} =\left(\gamma+\frac{\mathrm{1}}{\mathrm{2}{n}}\right)^{{m}+\mathrm{1}} +{o}\left(\frac{\mathrm{1}}{{n}}\right)=\gamma^{{m}+\mathrm{1}} +\left({m}+\mathrm{1}\right)\frac{\gamma^{{m}} }{\mathrm{2}{n}}+{o}\left(\frac{\mathrm{1}}{{n}}\right) \\…
Question Number 150095 by mathdanisur last updated on 09/Aug/21 $$\Omega\:=\int\:\frac{\mathrm{x}\:\mathrm{dx}}{\mathrm{x}^{\mathrm{8}} \:-\:\mathrm{1}}\:=\:? \\ $$ Answered by Ar Brandon last updated on 09/Aug/21 $$\Omega=\int\frac{{xdx}}{{x}^{\mathrm{8}} −\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{d}\left({x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} \right)^{\mathrm{4}}…
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Question Number 84528 by mr.perfected last updated on 14/Mar/20 $$\mathrm{1}=\mathrm{2} \\ $$ Commented by jagoll last updated on 14/Mar/20 $$\mathrm{one}\:\mathrm{man}\:\mathrm{have}\:\mathrm{2}\:\mathrm{wife} \\ $$$$\mathrm{haha} \\ $$ Commented…
Question Number 150058 by mathdanisur last updated on 09/Aug/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{cos}^{\mathrm{4}} \left(\mathrm{x}\right)\:+\:\mathrm{i}\:\mathrm{sin}^{\mathrm{4}} \left(\mathrm{x}\right)\:=\:\mathrm{4e}^{\mathrm{4}\boldsymbol{\mathrm{ix}}} \\ $$ Commented by MJS_new last updated on 10/Aug/21 $$\mathrm{I}\:\mathrm{found}\:\mathrm{these}\:\left({n}\in\mathbb{Z}\right): \\…
Question Number 150059 by mathdanisur last updated on 09/Aug/21 $$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}\centerdot\left(\mathrm{2n}\:+\:\mathrm{1}\right)}\:=\:? \\ $$ Answered by Kamel last updated on 09/Aug/21 $${S}=\mathrm{2}\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{2}{n}}−\frac{\mathrm{1}}{\mathrm{2}{n}+\mathrm{1}}\right)=\mathrm{2}\underset{{n}=\mathrm{1}} {\overset{+\infty}…
Question Number 84515 by M±th+et£s last updated on 13/Mar/20 $${Q}.{solve} \\ $$$${x}^{\mathrm{3}} −{x}={x}! \\ $$ Answered by mr W last updated on 13/Mar/20 $$\left({x}+\mathrm{1}\right){x}\left({x}−\mathrm{1}\right)={x}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)! \\…
Question Number 18979 by chernoaguero@gmail.com last updated on 02/Aug/17 Terms of Service Privacy Policy Contact: info@tinkutara.com