Question Number 157456 by tounghoungko last updated on 23/Oct/21 $$\:\int\:\mathrm{5}^{\mathrm{3}−\mathrm{2}{x}} \:{dx}\:=? \\ $$ Answered by FelipeLz last updated on 24/Oct/21 $$\int\mathrm{5}^{\mathrm{3}−\mathrm{2}{x}} {dx}\:=\:\mathrm{5}^{\mathrm{3}} \int\mathrm{5}^{−\mathrm{2}{x}} {dx} \\…
Question Number 157455 by aliibrahim1 last updated on 23/Oct/21 Answered by FongXD last updated on 23/Oct/21 $$\mathrm{let}\:\mathrm{u}=\mathrm{x}^{\mathrm{2021}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2021}} +._{._{._{.} } } }=\mathrm{x}^{\mathrm{2021}} +\frac{\mathrm{1}}{\mathrm{u}} \\ $$$$\Leftrightarrow\:\mathrm{u}^{\mathrm{2}}…
Question Number 91914 by M±th+et+s last updated on 03/May/20 $${hi}\:{every}\:{one}\:{here}\:{i}\:{will}\:{put}\:{my}\:{solution}\:\: \\ $$$${for}\:{old}\:{question}\:{by}\:{mr}.{MJS} \\ $$$$\int\frac{\sqrt{\left({x}−\mathrm{1}\right){x}\left({x}+\mathrm{1}\right)}}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}}{dx} \\ $$$$ \\ $$$${the}\:{solution}\:{by}\:{using}\:\:\: \\ $$$${Appell}\:{hypergeometric}\:{function} \\ $$ Answered by…
Question Number 91910 by Ar Brandon last updated on 03/May/20 $$\int\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \mathrm{x}\right)}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 03/May/20 $${let}\:{f}\left({a}\right)\:=\int\frac{{ln}\left(\mathrm{1}+{asin}^{\mathrm{2}}…
Question Number 157442 by bobhans last updated on 23/Oct/21 $$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{x}−\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{2}}}\: \\ $$ Answered by MJS_new last updated on 23/Oct/21 $$\int\frac{{dx}}{{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}}}= \\ $$$$\:\:\:\:\:\left[{t}={x}+\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}}\:\rightarrow\:{dx}=\frac{\sqrt{{x}^{\mathrm{2}}…
Question Number 91904 by Ar Brandon last updated on 03/May/20 $$\int_{\mathrm{1}} ^{\mathrm{e}^{\pi} } \frac{\mathrm{cos}\left(\mathrm{lnx}\right)}{\mathrm{x}}\mathrm{dx} \\ $$ Commented by Prithwish Sen 1 last updated on 03/May/20…
Question Number 26362 by abdo imad last updated on 24/Dec/17 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\propto} {e}^{−{x}} {lnx}\:{dx}\:\:\:{for}\:{that}\:{use} \\ $$$${A}_{{n}} \:\:=\:\:\:\int_{\mathrm{0}} ^{{n}} \:\left(\mathrm{1}−\:\frac{{t}}{{n}}\right)^{{n}−\mathrm{1}} {ln}\left({t}\right)\:{dt}\:\:. \\ $$ Terms of Service…
Question Number 26359 by abdo imad last updated on 24/Dec/17 $${find}\:\:\:{lim}_{{n}−>\propto} \:\:\int_{\mathrm{0}} ^{{n}} \:\left(\mathrm{1}−\frac{{t}}{{n}}\right)^{{n}−\mathrm{1}} {dt}\:\:\:. \\ $$ Commented by abdo imad last updated on 25/Dec/17…
Question Number 26360 by abdo imad last updated on 24/Dec/17 $$\:\:{find}\:{the}\:{value}\:{of}\:\:\:\:\int_{\mathrm{0}} ^{\:\propto\:} \:\frac{{cos}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:. \\ $$ Commented by abdo imad last updated on 25/Dec/17 $${let}\:{put}\:{I}=\:\:\int_{\mathrm{0}}…
Question Number 26357 by abdo imad last updated on 24/Dec/17 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left({cos}\theta\right){d}\theta\:\:{and}\: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left({sin}\theta\right){d}\theta\:\:\:. \\ $$ Commented by prakash jain last updated…