Question Number 111624 by mathdave last updated on 04/Sep/20 $${if}\:{x}\:{is}\:{a}\:{cube}\:{root}\:{of}\:{a}\:{unity} \\ $$$${prove}\:{that}\: \\ $$$$\left(\mathrm{1}−{x}\right)^{\mathrm{6}} =−\mathrm{27} \\ $$ Answered by Her_Majesty last updated on 04/Sep/20 $$\left(\mathrm{1}−\omega\right)^{\mathrm{6}}…
Question Number 111622 by mathdave last updated on 04/Sep/20 $${show}\:{that}\:{the}\:{close}\:{form}\:{of}\: \\ $$$$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\underset{{i}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\frac{\left(−\mathrm{1}\right)^{{k}+{i}} }{\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}{i}+\mathrm{2}\right)}\right]\right)=\frac{\mathrm{1}}{\mathrm{8}}\mathrm{ln2} \\ $$ Answered by mathdave last updated on…
Question Number 111620 by mathdave last updated on 04/Sep/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\Gamma\left({x}\right){dx}=\mathrm{ln}\sqrt{\mathrm{2}\pi} \\ $$ Answered by mathmax by abdo last updated on 04/Sep/20…
Question Number 111618 by mathdave last updated on 04/Sep/20 $${solve}\:{the}\:{fredholm}\:{integral}\:{equation}\:{of} \\ $$$${the}\:{second}\:{kind}\: \\ $$$${y}\left({x}\right)={x}+\lambda\int_{\mathrm{0}} ^{\mathrm{1}} \left({xt}^{\mathrm{2}} +{x}^{\mathrm{2}} {t}\right){y}\left({t}\right){dt} \\ $$ Terms of Service Privacy Policy…
Question Number 111616 by mathdave last updated on 04/Sep/20 $${solve}\:{the}\:{integral}\:{problem} \\ $$$$\int\frac{\mathrm{cos}{x}}{\mathrm{2}−\mathrm{sin2}{x}}{dx} \\ $$ Answered by Her_Majesty last updated on 05/Sep/20 $$\int\frac{\mathrm{cos}\:{x}}{\mathrm{2}−\mathrm{sin}\:\mathrm{2}{x}}{dx}= \\ $$$$\left(\mathrm{use}\:{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\right) \\…
Question Number 111619 by mathdave last updated on 05/Sep/20 $${solve}\:{for}\:{x}\:{in}\: \\ $$$${x}^{\mathrm{2}} +\mathrm{4}{x}=\sqrt{\mathrm{40}{x}^{\mathrm{2}} +\mathrm{8}{x}−\mathrm{16}} \\ $$ Commented by Her_Majesty last updated on 04/Sep/20 $${square}\:{it},\:{solve}\:{the}\:\mathrm{4}^{{th}} \:{degree}\:{polynomial}…
Question Number 111614 by mathdave last updated on 04/Sep/20 $${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{sin}{x}}{{x}}\right)^{\mathrm{7}} =\frac{\mathrm{5887}\pi}{\mathrm{23040}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 111617 by mathdave last updated on 04/Sep/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{ln}\left(\mathrm{2cos}^{\mathrm{2}} {x}\right)}{\mathrm{cos2}{x}}{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{16}} \\ $$ Answered by mathmax by abdo last updated…
Question Number 111610 by A8;15: last updated on 04/Sep/20 Commented by A8;15: last updated on 04/Sep/20 please help Commented by A8;15: last updated on 04/Sep/20 please…
Question Number 111615 by mathdave last updated on 04/Sep/20 $${solve} \\ $$$$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}\right)\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{3}}} \\ $$ Answered by mathmax by abdo last updated on 04/Sep/20…