Question Number 26563 by abdo imad last updated on 26/Dec/17 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}−{cosx}}{{x}^{\mathrm{2}} }\:{dx} \\ $$ Commented by abdo imad last updated on 28/Dec/17 $${let}\:{put}\:{I}=\:\int_{\mathrm{0}}…
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Question Number 26564 by abdo imad last updated on 26/Dec/17 $${let}\:{give}\:\Gamma\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} {t}^{{x}−\mathrm{1}} \:{e}^{−{t}} {dt}\:\:\:{and}\:\:\:{x}>\mathrm{0}\left({gamma}\:{euler}\:{function}\right) \\ $$$${prove}\:{that}\:\:\Gamma\left({x}\right)\:\:={lim}_{{n}−>\propto} \:\frac{\left({n}!\right)\:{n}^{{x}} }{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)…\left({n}+{x}\right)} \\ $$ Terms of Service Privacy…
Question Number 26559 by abdo imad last updated on 26/Dec/17 $${let}\:{put}\:{F}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{tx}} \:\frac{{sint}}{{t}}\:{dt}\:\:\:{with}\:\:{x}\geqslant\mathrm{0} \\ $$$${we}\:{accept}\:{that}\:{F}\:{is}\:{class}\:{C}^{\mathrm{1}} \:{on}\:\left[\mathrm{0},\propto\left[\right.\right. \\ $$$${calculate}\:\:\frac{\partial{F}}{\partial{x}}\:\:{and}\:{find}\:{F}\left({x}\right) \\ $$$${then}\:\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sint}}{{t}}\:{dt} \\ $$…
Question Number 26558 by abdo imad last updated on 26/Dec/17 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sinx}}{{x}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{dx} \\ $$ Commented by abdo imad last updated on 27/Dec/17 $${let}\:{put}\:\:{I}=\:\int_{\mathrm{0}}…
Question Number 92089 by mathmax by abdo last updated on 04/May/20 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({cosx}+{sinx}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92088 by mathmax by abdo last updated on 04/May/20 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({cosx}\right)\:\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{ln}\left({sinx}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92087 by mathmax by abdo last updated on 04/May/20 $$\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}}{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 92082 by mathmax by abdo last updated on 04/May/20 $${let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {x}\sqrt{{x}^{\mathrm{2}} −{x}+\alpha}{dx}\:\:\:\:\:\:{with}\:\alpha>\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\left.\mathrm{1}\right)\:{explicit}\:\:{f}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{xdx}}{\:\sqrt{{x}^{\mathrm{2}} −{x}+\alpha}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:{intehrals}\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 92081 by mathmax by abdo last updated on 04/May/20 $${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \left({x}^{\mathrm{3}} −\mathrm{3}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92078 by mathmax by abdo last updated on 04/May/20 $${calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{cos}\left({arctan}\left(\mathrm{2}{x}+\mathrm{1}\right)\right)}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx} \\ $$ Commented by abdomathmax last updated on 09/May/20 $${I}\:=\int_{−\infty}…