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Category: Integration

Question-60320

Question Number 60320 by Sardor2211 last updated on 19/May/19 Commented by maxmathsup by imad last updated on 20/May/19 $${let}\:{I}\:=\int\:\:\frac{{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} \:+\mathrm{5}{x}\:+\mathrm{23}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}−\mathrm{5}\right)}{dx}\:\:{let}\:{decompose}\:{F}\left({x}\right)\:=\frac{{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} \:+\mathrm{5}{x}\:+\mathrm{23}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}−\mathrm{5}\right)}…

Question-60318

Question Number 60318 by Sardor2211 last updated on 19/May/19 Commented by kaivan.ahmadi last updated on 20/May/19 $${we}\:{find}\:{I}=\int{x}^{\mathrm{2}} {arctgx}\:{dx}\:{then}\:{multiply}\:\mathrm{4} \\ $$$${u}={arctgx}\Rightarrow{du}=\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$${dv}={x}^{\mathrm{2}} {dx}\Rightarrow{v}=\frac{{x}^{\mathrm{3}} }{\mathrm{3}}…

Given-f-x-f-x-2-x-R-if-0-2-f-x-dx-k-then-0-1010-f-x-2a-dx-for-a-Z-

Question Number 125841 by bramlexs22 last updated on 14/Dec/20 $${Given}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right)\:\forall{x}\in\mathbb{R} \\ $$$${if}\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}{f}\left({x}\right){dx}={k}\:{then}\:\underset{\mathrm{0}} {\overset{\mathrm{1010}} {\int}}{f}\left({x}+\mathrm{2}{a}\right){dx}\:? \\ $$$${for}\:{a}\in\mathbb{Z}\: \\ $$ Commented by mr W last…

let-f-t-0-e-3-x-2-x-2-t-2-dx-with-t-gt-0-1-determine-a-explicit-form-of-f-t-2-find-also-g-t-0-e-3-x-2-x-2-t-2-2-dx-3-find-the-values-of-integrals-

Question Number 60264 by maxmathsup by imad last updated on 19/May/19 $${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−\mathrm{3}\:\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} }{dx}\:\:{with}\:{t}>\mathrm{0} \\ $$$$\mathrm{1}.\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\mathrm{2}.\:{find}\:{also}\:{g}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]}…

let-U-n-0-e-n-x-2-x-2-3-dx-1-calculate-U-n-interms-of-n-2-find-lim-n-n-U-n-3-determine-nature-of-the-serie-U-n-

Question Number 60263 by maxmathsup by imad last updated on 19/May/19 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−{n}\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} +\mathrm{3}}\:{dx}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{U}_{{n}} \\…