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Question Number 212461 by MrGaster last updated on 14/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{prove}: \\ $$$$\:\:\int_{\mathrm{0}} ^{+\infty} \frac{{dx}}{\:\sqrt{{x}^{\mathrm{4}} +\mathrm{25}{x}^{\mathrm{2}} +\mathrm{160}}}=\int_{\mathrm{0}} ^{+\infty} \frac{{dx}}{\:\sqrt{{x}^{\mathrm{4}} −\mathrm{95}{x}^{\mathrm{2}} +\mathrm{2560}}} \\ $$ Commented by Ghisom…
Question Number 212435 by Ar Brandon last updated on 13/Oct/24 Answered by mr W last updated on 13/Oct/24 $${y}'=−\frac{\mathrm{2}{y}^{\mathrm{2}} +{xy}}{{x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} } \\ $$$${let}\:{y}={px} \\…
Question Number 212358 by MrGaster last updated on 11/Oct/24 $$ \\ $$$$\:\:\:\:\:\int\int\int_{\mathbb{R}^{\mathrm{3}} } \frac{{e}^{−\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }} }{\left(\mathrm{1}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)}{dx}\:{dy}\:{dz} \\ $$ Terms of…
Question Number 212141 by MrGaster last updated on 03/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\int\frac{\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{dx}. \\ $$$$ \\ $$ Answered by BHOOPENDRA last updated on 03/Oct/24 $$\int\frac{\mathrm{cos}\:^{\mathrm{2}}…
Question Number 212107 by MrGaster last updated on 01/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}=\int_{\mathrm{0}} ^{\infty} \frac{{x}\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} }{dx}. \\ $$$$ \\ $$ Answered by Frix last updated on…
Question Number 211800 by MrGaster last updated on 21/Sep/24 $$ \\ $$$$\boldsymbol{{set}}\:\boldsymbol{\Omega}=\left\{\left(\boldsymbol{{x}},\boldsymbol{{y}},\boldsymbol{{z}}\right)\mid\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} \leq\mathrm{1}\right\}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{certificat}}\mathrm{e}: \\ $$$$\:\:\frac{\mathrm{4}\boldsymbol{\pi}}{\mathrm{3}}\sqrt[{\mathrm{3}}]{\mathrm{2}}\leq\int\underset{\boldsymbol{\Omega}} {\int}\int\sqrt[{\mathrm{3}}]{\boldsymbol{{x}}+\mathrm{2}\boldsymbol{{y}}−\mathrm{2}\boldsymbol{{z}}+\mathrm{5}}\boldsymbol{{dv}}\leq\frac{\mathrm{8}\boldsymbol{\pi}}{\mathrm{3}} \\ $$$$ \\ $$$$ \\…
Question Number 211738 by MrGaster last updated on 19/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{5}} +\mathrm{1}\:}\boldsymbol{{dx}}. \\ $$$$ \\ $$ Commented by Frix last updated on 19/Sep/24 $$=\int\frac{{dx}}{\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}}…
Question Number 211703 by MrGaster last updated on 17/Sep/24 $$ \\ $$$$\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{quadruple}\: \\ $$$$\mathrm{integralas}\:\mathrm{follows}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\boldsymbol{{x}}} \int_{\mathrm{0}} ^{\boldsymbol{\mathrm{y}}} \int_{\mathrm{0}} ^{\boldsymbol{{z}}} \frac{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}}…
Question Number 211579 by MrGaster last updated on 13/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\mathrm{1}}{\left(\mathrm{1}−\boldsymbol{{x}}^{\mathrm{4}} \right)\sqrt{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}} }}\boldsymbol{{dx}}. \\ $$$$ \\ $$ Answered by lepuissantcedricjunior last updated on 13/Sep/24…