Question Number 157655 by tounghoungko last updated on 26/Oct/21 $$\:\:{x}^{\mathrm{2}} \:{f}\left({x}^{\mathrm{3}} \right)+\frac{\mathrm{1}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }\:{f}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)=\mathrm{4}{x}^{\mathrm{3}} \left(\mathrm{1}+{x}^{\mathrm{4}} \right)^{\mathrm{5}} \\ $$$$\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} {f}\left({x}\right)\:{dx}\:=? \\ $$ Commented by cortano last…
Question Number 26575 by abdo imad last updated on 26/Dec/17 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−\left[{x}\right]} {sinxdx}\:\:\:{in}\:{that}\:\left[{x}\right]={E}\left({x}\right) \\ $$ Commented by abdo imad last updated on 29/Dec/17 $${let}\:{put}\:{I}=\:\int_{\mathrm{0}}…
Question Number 26569 by abdo imad last updated on 26/Dec/17 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}\:} {x}\:{E}\left(\frac{\mathrm{1}}{{x}}\right){dx}\: \\ $$ Commented by abdo imad last updated on 30/Dec/17 $${let}\:{put}\:{I}=\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 26570 by abdo imad last updated on 26/Dec/17 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} {e}^{−{px}} /{sinx}/{dx}\:\:\:{with}\:{p}>\mathrm{0} \\ $$ Commented by abdo imad last updated on 02/Jan/18 $${let}\:{put}\:{I}=\:\int_{\mathrm{0}}…
Question Number 26566 by abdo imad last updated on 26/Dec/17 $${let}\:{give}\:\Gamma\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:{t}^{{x}−\mathrm{1}} {e}^{−{t}} {dt}\:{with}\:{x}>\mathrm{0}\:{prove}\:{that} \\ $$$$\:{lim}\:_{{n}−>\propto} \int_{\mathrm{0}} ^{{n}} \:\left(\mathrm{1}−\frac{{t}}{{n}}\right)^{{n}} {t}^{{x}−\mathrm{1}} {dt}\:\:=\:\Gamma\left({x}\right) \\ $$ Commented…
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