Biết tích phân \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaaca % WG4bGaaiOlaiaadwgadaahaaWcbeqaaiaaikdacaWG4baaaOGaaeiz % aiaadIhaaSqaaiaaicdaaeaacaaIXaaaniabgUIiYdGccqGH9aqpda % WcaaqaaiaadwgadaahaaWcbeqaaiaadggaaaGccqGHRaWkcaWGIbaa % baGaaGinaaaaaaa!45ED! \int\limits_0^1 {x.{e^{2x}}{\rm{d}}x} = \frac{{{e^a} + b}}{4}\) với \(a,b \in Z\). Tính a +b

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaqaabe % qaaiaadwhacqGH9aqpcaWG4baabaGaaeizaiaadAhacqGH9aqpcaWG % LbWaaWbaaSqabeaacaaIYaGaamiEaaaakiaabsgacaWG4baaaiaawU % haaiabgkDiEpaaceaaeaqabeaacaqGKbGaamyDaiabg2da9iaabsga % caWG4baabaGaamODaiabg2da9maalaaabaGaaGymaaqaaiaaikdaaa % GaamyzamaaCaaaleqabaGaaGOmaiaadIhaaaaaaOGaay5Eaaaaaa!5062! \left\{ \begin{array}{l} u = x\\ {\rm{d}}v = {e^{2x}}{\rm{d}}x \end{array} \right. \Rightarrow \left\{ \begin{array}{l} {\rm{d}}u = {\rm{d}}x\\ v = \frac{1}{2}{e^{2x}} \end{array} \right.\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taam % ysaiabg2da9maapehabaGaamiEaiaac6cacaWGLbWaaWbaaSqabeaa % caaIYaGaamiEaaaakiaabsgacaWG4baaleaacaaIWaaabaGaaGymaa % qdcqGHRiI8aOGaeyypa0ZaaqGaaeaadaWcaaqaaiaaigdaaeaacaaI % YaaaaiaadIhacaWGLbWaaWbaaSqabeaacaaIYaGaaGPaVlaadIhaaa % aakiaawIa7amaaDaaaleaacaaIWaaabaGaaGymaaaakiabgkHiTmaa % pehabaWaaSaaaeaacaaIXaaabaGaaGOmaaaacaWGLbWaaWbaaSqabe % aacaaIYaGaamiEaaaakiaabsgacaWG4baaleaacaaIWaaabaGaaGym % aaqdcqGHRiI8aOGaeyypa0ZaaSaaaeaacaaIXaaabaGaaGOmaaaaca % WGLbWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0YaaSaaaeaacaaIXaaa % baGaaGinaaaacaGGOaGaamyzamaaCaaaleqabaGaaGOmaaaakiabgk % HiTiaaigdacaGGPaGaeyypa0ZaaSaaaeaacaWGLbWaaWbaaSqabeaa % caaIYaaaaOGaey4kaSIaaGymaaqaaiaaisdaaaaaaa!6BD1! \Rightarrow I = \int\limits_0^1 {x.{e^{2x}}{\rm{d}}x} = \left. {\frac{1}{2}x{e^{2\,x}}} \right|_0^1 - \int\limits_0^1 {\frac{1}{2}{e^{2x}}{\rm{d}}x} = \frac{1}{2}{e^2} - \frac{1}{4}({e^2} - 1) = \frac{{{e^2} + 1}}{4}\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taam % yyaiabgUcaRiaadkgacqGH9aqpcaaIYaGaey4kaSIaaGymaiabg2da % 9iaaiodaaaa!4022! \Rightarrow a + b = 2 + 1 = 3\)