Question Number 194759 by horsebrand11 last updated on 15/Jul/23 $$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\frac{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\right)\:\mathrm{dxdy}\: \\ $$ Commented by Frix last updated on…
Question Number 194785 by tri26112004 last updated on 15/Jul/23 $$\int\int\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:{dxdy}\:\left({D}={x}^{\mathrm{4}} +{y}^{\mathrm{4}} \leqslant\mathrm{1}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 194591 by horsebrand11 last updated on 11/Jul/23 $$\:\:\:\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\:\underset{\mathrm{2x}^{\mathrm{2}} } {\overset{\mathrm{8}} {\int}}\:\:\underset{−\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}−\mathrm{x}^{\mathrm{2}} }} {\overset{\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}−\mathrm{x}^{\mathrm{2}} }} {\int}}\:\left(\sqrt{\mathrm{3x}^{\mathrm{2}} +\mathrm{3z}^{\mathrm{2}} }\:\right)\mathrm{dzdydx} \\ $$ Terms of…
Question Number 194548 by horsebrand11 last updated on 09/Jul/23 Commented by horsebrand11 last updated on 09/Jul/23 $$\:\underline{\gtrdot^{} } \\ $$ Answered by AST last updated…
Question Number 194515 by Kamel last updated on 08/Jul/23 $$\mid\int{f}\left({x}\right){dx}\mid=\int\mid{f}\left({x}\right)\mid{dx} \\ $$ Answered by witcher3 last updated on 11/Jul/23 $$\mathrm{what}\:\mathrm{information}?\mathrm{about}\:\mathrm{f}\:\mathrm{continus}\:\mathrm{or}\:\mathrm{by}\:\mathrm{part}? \\ $$ Terms of Service…
Question Number 194456 by horsebrand11 last updated on 07/Jul/23 $$\:\:\:\:\:\:\cancel{ } \\ $$ Answered by cortano12 last updated on 07/Jul/23 $$\:\:\:\underbrace{\lesseqgtr} \\ $$ Answered by…
Question Number 194388 by SaRahAli last updated on 05/Jul/23 $$\int\frac{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\mathrm{sin}\:{x}+\mathrm{4cos}\:{x}}{\mathrm{2}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 194412 by SaRahAli last updated on 05/Jul/23 Answered by som(math1967) last updated on 05/Jul/23 $$\:\int{ln}\left({lnx}\right){dx}+\int\frac{{dx}}{\left({lnx}\right)^{\mathrm{2}} } \\ $$$$={ln}\left({lnx}\right)\int{dx}−\int\left\{\frac{{d}}{{dx}}{ln}\left({lnx}\right)\int{dx}\right\}{dx} \\ $$$$\:\:+\int\frac{{dx}}{\left({lnx}\right)^{\mathrm{2}} } \\ $$$$={xln}\left({lnx}\right)−\int\frac{{xdx}}{{xlnx}}\:+\int\frac{{dx}}{\left({lnx}\right)^{\mathrm{2}}…
Question Number 193982 by cortano12 last updated on 25/Jun/23 $$\:\:\:\:\:\int\:\frac{\mathrm{6x}^{\mathrm{3}} +\mathrm{9x}^{\mathrm{2}} +\mathrm{15x}+\mathrm{6}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}}\:\mathrm{dx}\:=? \\ $$ Answered by MM42 last updated on 26/Jun/23 $${I}=\left({ax}^{\mathrm{2}} +{bx}+{e}\right)\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}+{f}\int\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 193852 by SaRahAli last updated on 21/Jun/23 Answered by cortano12 last updated on 21/Jun/23 $$\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\int\:\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{cos}\:\left(\mathrm{x}−\frac{\pi}{\mathrm{4}}\right)}=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\int\:\frac{\mathrm{cos}\:\mathrm{2u}}{\mathrm{cos}\:\mathrm{u}}\:\mathrm{du} \\ $$$$\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\int\:\frac{\mathrm{2cos}\:^{\mathrm{2}} \mathrm{u}−\mathrm{1}}{\mathrm{cos}\:\mathrm{u}}\:\mathrm{du} \\ $$$$\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\left[\int\:\mathrm{2cos}\:\mathrm{u}\:\mathrm{du}−\int\mathrm{sec}\:\mathrm{u}\:\mathrm{du}\:\right] \\ $$$$\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\left[\:\mathrm{2sin}\:\mathrm{u}−\mathrm{ln}\:\mid\mathrm{sec}\:\mathrm{u}+\mathrm{tan}\:\mathrm{u}\mid\:+\mathrm{c}\:\right. \\…