Question Number 130011 by mnjuly1970 last updated on 21/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\Phi=\underset{\:\:\:\:\:\mathbb{R}} {\int}{e}^{\left(−{e}^{{x}} +\mathrm{2}{x}\right)} {x}^{\mathrm{2}} {dx}=\left(\mathrm{1}−\gamma\right)^{\mathrm{2}} +\frac{\pi^{\mathrm{2}} −\mathrm{6}}{\mathrm{6}} \\ $$$$ \\ $$ Answered…
Question Number 130006 by Adel last updated on 21/Jan/21 Answered by Dwaipayan Shikari last updated on 21/Jan/21 $${S}={x}+\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}^{\mathrm{3}} +…. \\ $$$${S}\left(\mathrm{1}−{x}\right)={x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +… \\…
Question Number 64471 by mmkkmm000m last updated on 18/Jul/19 $$\int\sqrt[{\mathrm{4}}]{{tanx}}{dx} \\ $$ Answered by MJS last updated on 18/Jul/19 $$\int\sqrt[{\mathrm{4}}]{\mathrm{tan}\:{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt[{\mathrm{4}}]{\mathrm{tan}\:{x}}\:\rightarrow\:{dx}=\mathrm{4}\sqrt[{\mathrm{4}}]{\mathrm{tan}^{\mathrm{3}} \:{x}}\:\mathrm{cos}^{\mathrm{2}} \:{x}\:{dt}\right] \\…
Question Number 64469 by Tawa1 last updated on 18/Jul/19 Answered by MJS last updated on 18/Jul/19 $$\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{incircle}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rectangular} \\ $$$$\mathrm{triangle}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$${r}=\frac{{a}+{b}−\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }}{\mathrm{2}} \\ $$$$\frac{{a}+{b}−\sqrt{{a}^{\mathrm{2}}…
Question Number 64465 by Theophilus111 last updated on 18/Jul/19 $${vy} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 129998 by Eric002 last updated on 21/Jan/21 $${what}\:{is}\:{fractional}\:{derivative}? \\ $$ Answered by Olaf last updated on 21/Jan/21 $$\mathrm{Generalization}\:\mathrm{of}\:\mathrm{the}\:\mathrm{derivative} \\ $$$$\mathrm{for}\:\alpha\:\in\mathbb{R}\::\:{D}^{\alpha} {f}\:=\:{f}^{\left(\alpha\right)} \left({x}\right) \\…
Question Number 64463 by aliesam last updated on 18/Jul/19 $$\int\sqrt{{sec}\left({x}\right)}\:{dx} \\ $$ Commented by Tony Lin last updated on 18/Jul/19 $$\int\sqrt{{secx}}{dx} \\ $$$$=\int\frac{{dx}}{\:\sqrt{{cosx}}}\: \\ $$$$=\int\frac{{dx}}{\:\sqrt{\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}}…
Question Number 129996 by Eric002 last updated on 21/Jan/21 $$\int\frac{\sqrt[{\mathrm{5}}]{{x}^{\mathrm{2}} }}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}+\sqrt{{x}^{\mathrm{5}} }}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 129997 by mohammad17 last updated on 21/Jan/21 $${prove}\:{that}\:\left[\left({cos}\left({n}\right)+{sin}\left({n}\right)\right)/{n}\right]\:{converge}\:{sequence} \\ $$ Answered by Dwaipayan Shikari last updated on 21/Jan/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cosn}+{sinn}}{{n}}=\frac{\mathrm{1}}{\mathrm{2}}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{e}^{{in}}…
Question Number 64459 by Tawa1 last updated on 18/Jul/19 Commented by Tony Lin last updated on 18/Jul/19 $${AR}={AP}=\mathrm{2},{RC}={QC}=\mathrm{5} \\ $$$${letPB}={BQ}={x} \\ $$$${cos}\mathrm{60}°=\frac{\left(\mathrm{2}+{x}\right)^{\mathrm{2}} +\left(\mathrm{5}+{x}\right)^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} }{\mathrm{2}\left(\mathrm{2}+{x}\right)\left(\mathrm{5}+{x}\right)}…