Question Number 107596 by Rio Michael last updated on 11/Aug/20 $$\mathrm{Given}\: \\ $$$$\:{I}_{{m},{n}} \:=\:\underset{\mathrm{1}} {\overset{{e}} {\int}}{x}^{{m}} \:\left(\mathrm{ln}\:{x}\right)^{{n}} \:{dx}\:\mathrm{where}\:{m},{n}\:\in\:\mathbb{N}^{\ast} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\left(\mathrm{1}\:+\:{m}\right){I}_{{m},{n}} \:=\:{e}^{{m}+\mathrm{1}} −{nI}_{{m},{n}−\mathrm{1}} \:\mathrm{for}\:{m}\:>\mathrm{0}\:\mathrm{and}\:{n}>\mathrm{0} \\ $$$$\mathrm{also},\:\mathrm{evaluate}\:{I}_{\mathrm{2},\mathrm{3}}…
Question Number 42054 by SammyKT last updated on 17/Aug/18 Commented by math khazana by abdo last updated on 17/Aug/18 $${what}\:{s}\:{C}?\:{C}\:{is}\:{not}\:{given}\:! \\ $$ Answered by tanmay.chaudhury50@gmail.com…
Question Number 107591 by hgrocks last updated on 11/Aug/20 Commented by hgrocks last updated on 11/Aug/20 $$\mathrm{Pls}\:\mathrm{Tell}\:\mathrm{Me}\:\mathrm{Which}\:\mathrm{one}\:\mathrm{is}\:\mathrm{correct} \\ $$$$\mathrm{and}\:\mathrm{why}\: \\ $$ Commented by hgrocks last…
Question Number 107567 by Ar Brandon last updated on 11/Aug/20 $$\int\sqrt{\mathrm{3x}^{\mathrm{2}} −\mathrm{2x}}\:\mathrm{dx} \\ $$ Answered by bobhans last updated on 11/Aug/20 $$\int\:\sqrt{\mathrm{3x}^{\mathrm{2}} −\mathrm{2x}}\:\mathrm{dx}\:=\:\int\sqrt{\mathrm{3}\left(\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{2x}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{9}}\right)−\frac{\mathrm{1}}{\mathrm{3}}}\:\mathrm{dx} \\…
Question Number 42012 by rahul 19 last updated on 16/Aug/18 $$\mathrm{Solve}\:: \\ $$$$\frac{{d}\mathrm{u}}{{d}\mathrm{t}}\:=\:\frac{\mathrm{3u}−\mathrm{7t}}{−\mathrm{7u}+\mathrm{3t}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 16/Aug/18 $${method}\:\mathrm{1} \\ $$$${this}\:{method}\:{for}\:{homogeneous}\:{equation}…
Question Number 173068 by mnjuly1970 last updated on 06/Jul/22 Answered by Mathspace last updated on 06/Jul/22 $$\Phi=\int_{\mathrm{0}} ^{\infty} \left(\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} {sin}\left({x}+{y}\right){dx}\right){e}^{−{y}} {dy} \\ $$$${but}\:\int_{\mathrm{0}}…
Question Number 41989 by Raj Singh last updated on 16/Aug/18 Commented by maxmathsup by imad last updated on 16/Aug/18 $${let}\:\:{I}\:\:=\:\int\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{2}\right)^{\mathrm{3}} }\:\:{changement}\:{x}=\sqrt{\mathrm{2}}{tan}\left({t}\right)\:{give} \\ $$$${I}\:\:=\:\int\:\:\:\:\frac{\sqrt{\mathrm{2}}\left(\mathrm{1}+{tan}^{\mathrm{2}} {t}\right)}{\mathrm{8}\left(\mathrm{1}+{tan}^{\mathrm{2}}…
Question Number 107515 by mohammad17 last updated on 11/Aug/20 $$\int\frac{{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{8}} }{dx} \\ $$ Answered by Ar Brandon last updated on 11/Aug/20 $$\mathrm{I}=\int\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{1}+\mathrm{x}^{\mathrm{8}} }\mathrm{dx}…
Question Number 173005 by Mikenice last updated on 04/Jul/22 Commented by MJS_new last updated on 05/Jul/22 $$\mathrm{you}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{above}\:\mathrm{functions} \\ $$$$\mathrm{is}\:\mathrm{continuous}\:\mathrm{but}\:\mathrm{you}\:\mathrm{want}\:\mathrm{to}\:\mathrm{solve}\:{this}?! \\ $$ Terms of Service Privacy…
Question Number 172996 by Mathspace last updated on 04/Jul/22 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{{n}} }{ln}^{\mathrm{2}} {xdx} \\ $$$$\left.\mathrm{1}\right){lim}\:{U}_{{n}} ? \\ $$$$\left.\mathrm{2}\right){equivalent}\:{of}\:{U}_{{n}} \left({n}\rightarrow\infty\right) \\ $$ Answered by…