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Category: Integration

nice-calculus-prove-that-0-1-log-1-x-x-2-dx-2-2-

Question Number 137829 by mnjuly1970 last updated on 07/Apr/21 $$\:\:\:\:\:…….{nice}\:\:…\:…\:….\:{calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:{that}\::::: \\ $$$$\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{log}\left(\mathrm{1}−{x}\right)}{{x}}\right)^{\mathrm{2}} {dx}=\mathrm{2}\zeta\left(\mathrm{2}\right)…. \\ $$$$ \\ $$ Answered by EnterUsername last…

If-z-x-is-a-complex-function-is-the-following-true-zdx-z-dx-i-z-dx-

Question Number 6737 by FilupSmith last updated on 19/Jul/16 $$\mathrm{If}\:{z}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{function}, \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{following}\:\mathrm{true}: \\ $$$$\int{zdx}=\int\Re\left({z}\right){dx}+{i}\int\Im\left({z}\right){dx} \\ $$ Commented by prakash jain last updated on 19/Jul/16 $$\mathrm{Yes}.\:\mathrm{Since}\:{i}\:\mathrm{is}\:\mathrm{simply}\:\mathrm{a}\:\mathrm{constant}.…

mathematical-analysis-evaluate-0-1-ln-2-1-x-2-x-

Question Number 137799 by mnjuly1970 last updated on 06/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…..\:{mathematical}\:..\:…\:…\:{analysis}…. \\ $$$$\:\:\:\:\:\:\:{evaluate}\:::\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{{x}}\right)=? \\ $$$$ \\ $$ Answered…

yz-dx-xz-dy-xy-dz-pleas-sir-help-me-

Question Number 72259 by mhmd last updated on 26/Oct/19 $$\int{yz}\:{dx}\:+\int{xz}\:{dy}\:+\int{xy}\:{dz}\:\:\:\:{pleas}\:{sir}\:{help}\:{me}\:? \\ $$ Answered by MJS last updated on 26/Oct/19 $$…={yz}\int{dx}+{xz}\int{dy}+{xy}\int{dz}=\mathrm{3}{xyz} \\ $$$$\mathrm{all}\:\mathrm{variables}\:\neq\:\mathrm{the}\:\mathrm{integral}\:\mathrm{variable}\:\mathrm{are} \\ $$$$\mathrm{considered}\:\mathrm{as}\:\mathrm{constant}\:\mathrm{factors} \\…

dx-sinx-sin2x-dx-

Question Number 6710 by Tawakalitu. last updated on 15/Jul/16 $$\int\:\frac{{dx}}{{sinx}\:+\:{sin}\mathrm{2}{x}}\:{dx} \\ $$ Answered by Yozzii last updated on 15/Jul/16 $${I}=\int\frac{{dx}}{{sinx}+{sin}\mathrm{2}{x}}=\int\frac{{sinx}}{{sin}^{\mathrm{2}} {x}\left(\mathrm{1}+\mathrm{2}{cosx}\right)}{dx} \\ $$$${I}=\int\frac{−{sinx}}{−\left(\mathrm{1}−{cos}^{\mathrm{2}} {x}\right)\left(\mathrm{1}+\mathrm{2}{cosx}\right)}{dx} \\…