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Question Number 64327 by Chi Mes Try last updated on 16/Jul/19 $$\frac{{d}}{{dx}}\:\:\left(\:\underset{{f}\left({x}\right)} {\overset{{g}\left({x}\right)} {\int}}\:\phi\left({t}\right)\:{dt}\:\right)\:= \\ $$ Commented by mathmax by abdo last updated on 16/Jul/19…

Question Number 64268 by Chi Mes Try last updated on 16/Jul/19 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}^{\mathrm{99}} +\mathrm{2}^{\mathrm{99}} +…+\:{n}^{\mathrm{99}} }{{n}^{\mathrm{100}} }\:= \\ $$ Commented by Prithwish sen last updated…

Question Number 64267 by Chi Mes Try last updated on 16/Jul/19 $$\mathrm{If}\:\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:\:\frac{\mathrm{1}}{{a}+{b}\:\mathrm{cos}\:{x}}\:{dx},\:{a}>\mathrm{0}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\frac{\pi}{\:\sqrt{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }}\:, \\ $$$$\mathrm{then}\:\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:\:\:\frac{\mathrm{1}}{\left({a}+{b}\:\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:{dx}\:= \\ $$ Commented by…

Question Number 64225 by mmkkmm000m last updated on 16/Jul/19 $$\mathrm{Solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\underset{\:\sqrt{\mathrm{2}}} {\overset{{x}} {\int}}\:\:\:\frac{{dx}}{{x}\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:=\:\frac{\pi}{\mathrm{12}}\:\:\mathrm{is}\:\:{x}\:=\:\_\_\_\_\_. \\ $$ Answered by ajfour last updated on 16/Jul/19 $$\mathrm{cos}^{−\mathrm{1}}…

Question Number 64080 by Chi Mes Try last updated on 12/Jul/19 $$\int\frac{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}{\:\sqrt{\mathrm{1}−\mathrm{sin}\:\mathrm{2}{x}}}\:{e}^{\mathrm{sin}\:{x}} \mathrm{cos}\:{x}\:{dx}\:= \\ $$ Commented by som(math1967) last updated on 13/Jul/19 $${e}^{{sinx}} +{c} \\…