Question Number 129418 by mnjuly1970 last updated on 15/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…{advsnced}\:\:\:\:\:\:{calculus}….\:\: \\ $$$$ \\ $$$$\:\:\:{calculate}:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} {e}^{−\sqrt{{x}}\:} {ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{x}}\:}\right){dx} \\ $$$$ \\ $$ Answered by Dwaipayan Shikari…
Question Number 63883 by mmkkmm000m last updated on 10/Jul/19 $$\int{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}−\mathrm{2}{x}\right){dx} \\ $$ Commented by mathmax by abdo last updated on 12/Jul/19 $${let}\:{A}\:=\int\:{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right){ln}\left(\mathrm{1}−\mathrm{2}{x}\right)\:{dx}\:\:{we}\:{have} \\ $$$${ln}^{'} \left(\mathrm{1}−{u}\right)\:=−\frac{\mathrm{1}}{\mathrm{1}−{u}}\:=−\sum_{{n}=\mathrm{0}}…
Question Number 129419 by mathocean1 last updated on 15/Jan/21 $${Calculate} \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{+} } {{lim}}\mathrm{2}{ln}−\mathrm{1}+\frac{\mathrm{1}}{{x}}\:{and}\:\underset{{x}\rightarrow\mathrm{0}^{+} } {{lim}}\frac{{x}}{\mathrm{2}}\:+\:\frac{\mathrm{1}+{lnx}}{{x}} \\ $$$${Detail}\:{if}\:{possible}\:{sirs} \\ $$ Terms of Service Privacy Policy…
Question Number 63881 by mmkkmm000m last updated on 10/Jul/19 $$\int{e}^{{x}} /{Lnxdx} \\ $$ Commented by mathmax by abdo last updated on 11/Jul/19 $${let}\:{A}\:=\int\:\frac{{e}^{{x}} }{{lnx}}{dx}\:\:{changement}\:{lnx}\:={t}\:{give} \\…
Question Number 129413 by ZiYangLee last updated on 15/Jan/21 $$\mathrm{Let}\:\mathrm{a}\:\mathrm{sequence}\:\left\{{a}_{{n}} \right\}\:\mathrm{satisfies} \\ $$$$\:\:\:\:\begin{cases}{\:\:\:\:\:\:\:\:\:\:\:\:{a}_{\mathrm{1}} =\mathrm{1}}\\{{na}_{{n}} ={n}+\mathrm{2}\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}{a}_{{k}} ,\:{n}>\mathrm{2}}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a}_{\mathrm{2021}} . \\ $$ Commented by…
Question Number 129409 by Algoritm last updated on 15/Jan/21 Commented by soumyasaha last updated on 15/Jan/21 $$\:\:\:=\:\frac{\mathrm{4}}{\mathrm{9}}\left[\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{9}.\mathrm{11}}+\frac{\mathrm{1}}{\mathrm{9}^{\mathrm{2}} .\mathrm{11}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{9}^{\mathrm{3}} .\mathrm{11}^{\mathrm{3}} }+…\right] \\ $$$$\:\:\:=\:\frac{\mathrm{4}}{\mathrm{9}}\left[\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{99}}+\left(\frac{\mathrm{1}}{\mathrm{99}}\right)^{\mathrm{2}} \:+\left(\frac{\mathrm{1}}{\mathrm{99}}\right)^{\mathrm{3}} +…\right]…
Question Number 129404 by bemath last updated on 15/Jan/21 $$\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{cos}\:\theta−{i}\:\mathrm{sin}\:\theta}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{{i}}{\mathrm{2}}.\mathrm{cot}\:\left(\frac{\theta}{\mathrm{2}}\right) \\ $$$$\mathrm{prove}. \\ $$ Answered by MJS_new last updated on 15/Jan/21 $$\theta=\mathrm{2}\alpha \\ $$$$\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}\alpha\:−\mathrm{i}\:\mathrm{sin}\:\mathrm{2}\alpha\right)^{−\mathrm{1}} =…
Question Number 129403 by bemath last updated on 15/Jan/21 $$\:\mathrm{f}\left(\mathrm{n}\right)\:=\:\mathrm{4f}\left(\mathrm{n}−\mathrm{1}\right)\:−\mathrm{4f}\left(\mathrm{n}−\mathrm{2}\right)\:+\:\mathrm{n}^{\mathrm{2}} \: \\ $$$$\mathrm{and}\:\mathrm{f}\left(\mathrm{0}\right)=\mathrm{2}\:,\:\mathrm{f}\left(\mathrm{1}\right)=\mathrm{5}\: \\ $$ Commented by talminator2856791 last updated on 15/Jan/21 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{question}? \\ $$…
Question Number 129400 by SOMEDAVONG last updated on 15/Jan/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by MJS_new last updated on 15/Jan/21 $$\mathrm{in}\:\mathrm{cases}\:\mathrm{like}\:\mathrm{this}\:\mathrm{one}\:\mathrm{I}\:\mathrm{use}\:{Ostrogradski}'{s}…
Question Number 129394 by liberty last updated on 15/Jan/21 $$\begin{cases}{\mathrm{x}^{\mathrm{3}} −\mathrm{3x}^{\mathrm{2}} +\mathrm{5x}+\mathrm{17}=\mathrm{0}}\\{\mathrm{y}^{\mathrm{3}} −\mathrm{3y}^{\mathrm{2}} +\mathrm{5y}+\mathrm{11}=\mathrm{0}}\end{cases} \\ $$$$\:\mathrm{find}\:\mathrm{x}+\mathrm{y}\:. \\ $$ Answered by bemath last updated on 15/Jan/21…