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…
Question Number 111611 by mathdave last updated on 04/Sep/20 $${solve}\:{for}\:{x}\:{ad}\:{y}\:{in} \\ $$$$\mathrm{5}{x}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right)=\mathrm{12}………\left(\mathrm{1}\right) \\ $$$$\mathrm{5}{y}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right)=\mathrm{4}……….\left(\mathrm{2}\right) \\ $$ Answered by Her_Majesty last updated…
Question Number 177133 by Matica last updated on 01/Oct/22 $$\:\:{f}\left({x}\right)\:=\:{x}^{\mathrm{2022}} \:.\:{Find}\:\:{derivative}\:{f}^{\left({n}\right)} . \\ $$ Answered by JDamian last updated on 01/Oct/22 $${f}^{\left({n}\right)} =\begin{cases}{\frac{\mathrm{2022}!}{\left(\mathrm{2022}−{n}\right)!}\:{x}^{\mathrm{2022}−{n}} \:\:\:\:\:\forall{n}\leqslant\mathrm{2022}}\\{\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\forall{n}>\mathrm{2022}}\end{cases} \\…
Question Number 177134 by DAVONG last updated on 01/Oct/22 $$\mathrm{I}=\int\mathrm{ln}\left(\mathrm{1}+\mathrm{2e}^{−\mathrm{2x}} \right)\mathrm{dx}=? \\ $$ Answered by Frix last updated on 02/Oct/22 $$\int\mathrm{ln}\:\left(\mathrm{1}+\mathrm{2e}^{−\mathrm{2}{x}} \right)\:{dx}\overset{{t}=−\mathrm{2e}^{−\mathrm{2}{x}} } {=} \\…