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…
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 $$…={yz}\int{dx}+{xz}\int{dy}+{xy}\int{dz}=\mathrm{3}{xyz} \\ $$$$\mathrm{all}\:\mathrm{variables}\:\neq\:\mathrm{the}\:\mathrm{integral}\:\mathrm{variable}\:\mathrm{are} \\ $$$$\mathrm{considered}\:\mathrm{as}\:\mathrm{constant}\:\mathrm{factors} \\…
Question Number 6710 by Tawakalitu. last updated on 15/Jul/16 $$\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} \\ $$$${I}=\int\frac{−{sinx}}{−\left(\mathrm{1}−{cos}^{\mathrm{2}} {x}\right)\left(\mathrm{1}+\mathrm{2}{cosx}\right)}{dx} \\…
Question Number 6709 by Tawakalitu. last updated on 15/Jul/16 $$\int_{\mathrm{3}} ^{\mathrm{6}} \:\:\frac{\mathrm{22}\:−\:\mathrm{5}{x}^{\mathrm{3}} \:−\:\mathrm{5}{x}^{\mathrm{4}} }{\left({x}\:−\:\mathrm{1}\right)\left({x}\:+\:\mathrm{2}\right)}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 6699 by jose14918645@gmail.com last updated on 14/Jul/16 $$\int\left({e}^{{x}} +\mathrm{1}\right){e}^{{x}} {dx} \\ $$ Answered by FilupSmith last updated on 14/Jul/16 $$=\int{e}^{\mathrm{2}{x}} +{e}^{{x}} {dx} \\…
Question Number 6700 by jose14918645@gmail.com last updated on 14/Jul/16 $$\int\left({e}^{−\mathrm{2}+\mathrm{2}} {xdx}\right. \\ $$ Answered by FilupSmith last updated on 15/Jul/16 $$=\int{e}^{\mathrm{0}} {xdx} \\ $$$$=\int{xdx} \\…
Question Number 137770 by peter frank last updated on 06/Apr/21 Answered by Ñï= last updated on 06/Apr/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\int_{\mathrm{0}} ^{\mathrm{1}} {da}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}}{\left(\mathrm{1}+{ax}\right)\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 6686 by FilupSmith last updated on 13/Jul/16 $$\mathrm{Show}\:\mathrm{that}: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} {e}^{−{ix}^{\mathrm{2}} } {dx}=\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{{i}}{\mathrm{2}}\right)\sqrt{\frac{\pi}{\mathrm{2}}} \\ $$ Commented by FilupSmith last updated on 14/Jul/16…
Question Number 6665 by Yozzii last updated on 10/Jul/16 $$\int_{\mathrm{0}} ^{\mathrm{1}} {sinh}^{\mathrm{1}/{n}} {x}\:{dx}=?\:,\:{n}\in\mathbb{N} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 137717 by mnjuly1970 last updated on 05/Apr/21 Commented by Dwaipayan Shikari last updated on 05/Apr/21 $${f}\left({a}\right)=\frac{\mathrm{1}}{\mathrm{2}}\Gamma\left(\frac{{a}+\mathrm{1}}{\mathrm{2}}\right)\Gamma\left(\frac{\mathrm{3}−{a}}{\mathrm{2}}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}−{a}}{\mathrm{2}}\right)\Gamma\left(\frac{{a}+\mathrm{1}}{\mathrm{2}}\right)\Gamma\left(\frac{\mathrm{1}−{a}}{\mathrm{2}}\right)=\frac{\mathrm{1}−{a}}{\mathrm{4}}.\frac{\pi}{{sin}\left(\frac{\pi}{\mathrm{2}}+\frac{\pi}{\mathrm{2}}{a}\right)} \\ $$$$=\frac{\pi}{\mathrm{4}}\left(\mathrm{1}−{a}\right){sec}\left(\frac{\pi}{\mathrm{2}}{a}\right) \\ $$$$−\frac{\mathrm{1}}{\mathrm{3}}{f}'\left(\mathrm{0}\right)=\frac{\pi}{\mathrm{12}} \\ $$ Terms…