Question Number 161839 by mathmax by abdo last updated on 23/Dec/21 $$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{2}\right)^{\mathrm{2}} } \\ $$ Answered by ArielVyny last updated on 23/Dec/21…
Question Number 30766 by abdo imad last updated on 25/Feb/18 $${find}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\:\frac{{x}}{\:\sqrt{{x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30764 by abdo imad last updated on 25/Feb/18 $${let}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:\left(\mathrm{1}−\mathrm{2}{t}\right)^{{n}} \:{e}^{−{t}} {dt}\:\:{with}\:{n}\:{integr}\:{not}\:\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\forall{t}\in\left[\mathrm{0},\frac{\mathrm{1}}{\mathrm{2}}\right] \\ $$$$\frac{\mathrm{1}}{\:\sqrt{{e}}}\left(\mathrm{1}−\mathrm{2}{t}\right)^{{n}} \leqslant\:\left(\mathrm{1}−\mathrm{2}{t}\right)^{{n}} \:{e}^{−{t}} \:\leqslant\left(\mathrm{1}−\mathrm{2}{t}\right)^{{n}} \:{then}\:{find}\:{lim}_{{n}\rightarrow\infty\:} {I}_{{n}}…
Question Number 30765 by abdo imad last updated on 25/Feb/18 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}}}\:. \\ $$ Commented by abdo imad last updated on 26/Feb/18 $${we}\:{have}\:{x}^{\mathrm{2}}…
Question Number 30761 by abdo imad last updated on 25/Feb/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:{x}^{\mathrm{2}{n}+\mathrm{1}} \:{e}^{−{x}^{\mathrm{2}} } {dx}\:\:\:{with}\:{n}\:{from}\:{N}. \\ $$ Commented by abdo imad last updated on…
Question Number 30760 by abdo imad last updated on 25/Feb/18 $${find}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\left({lnx}\right)^{{n}} \:{dx}\:\:{with}\:{n}\:{fromN} \\ $$ Commented by abdo imad last updated on 27/Feb/18…
Question Number 161830 by EnterUsername last updated on 22/Dec/21 $$\int\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{14}} }} \\ $$ Answered by Ar Brandon last updated on 22/Dec/21 $$\mathrm{arcsin}\left({x}\right)=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)_{{n}}…
Question Number 96280 by bobhans last updated on 31/May/20 Commented by bemath last updated on 31/May/20 $$\mathrm{let}\:\mathrm{w}\:=\:\mathrm{arctan}\:\mathrm{x} \\ $$$$\mathrm{dw}\:=\:\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\Rightarrow\:\int\:\mathrm{w}\:\mathrm{dw}\:=\:\left[\frac{\mathrm{1}}{\mathrm{2}}\mathrm{w}^{\mathrm{2}} \:\right]_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\pi}{\mathrm{2}}\right)^{\mathrm{2}} =\:\frac{\pi^{\mathrm{2}}…
Question Number 30741 by abdo imad last updated on 25/Feb/18 $${let}\:{give}\:{D}=\:{R}_{+} ^{\mathrm{2}} \:−\left\{\left(\mathrm{0},\mathrm{0}\right)\right\}\:{and}\:\alpha\:{from}\:{R}\:{let} \\ $$$${C}_{\mathrm{1}} =\left\{\left({x},{y}\right)\in\:{D}/\mathrm{0}<{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \leqslant\mathrm{1}\:\right\} \\ $$$${C}_{\mathrm{2}} \:=\left\{\left({x},{y}\right)\:\in{D}\:/\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \geqslant\mathrm{1}\right\}\:{study}\:{the}\:{convergence}\:{of} \\ $$$${I}=\:\int\int_{{C}_{\mathrm{1}}…
Question Number 30737 by NECx last updated on 25/Feb/18 $$\int\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{ln}\:{x}}{dx} \\ $$ Commented by NECx last updated on 25/Feb/18 $${is}\:{this}\:{possible}? \\ $$ Terms of…