Tích phân \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiabg2 % da9maapehabaGaamiEaiaac6cacaqGLbWaaWbaaSqabeaacaaIYaGa % amiEaaaakiaabsgacaWG4baaleaacaaIWaaabaGaaGOmaaqdcqGHRi % I8aaaa!4212! I = \int\limits_0^2 {x.{{\rm{e}}^{2x}}{\rm{d}}x} \) là 

Đặt \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaqaabe % qaaiaadwhacqGH9aqpcaWG4baabaGaaeizaiaadAhacqGH9aqpcaqG % LbWaaWbaaSqabeaacaaIYaGaamiEaaaakiaabsgacaWG4baaaiaawU % haaaaa!41B5! \left\{ \begin{array}{l} u = x\\ {\rm{d}}v = {{\rm{e}}^{2x}}{\rm{d}}x \end{array} \right.\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H49aai % qaaqaabeqaaiaabsgacaWG1bGaeyypa0JaaeizaiaadIhaaeaacaWG % 2bGaeyypa0ZaaSaaaeaacaaIXaaabaGaaGOmaaaacaqGLbWaaWbaaS % qabeaacaaIYaGaamiEaaaaaaGccaGL7baaaaa!449C! \Rightarrow \left\{ \begin{array}{l} {\rm{d}}u = {\rm{d}}x\\ v = \frac{1}{2}{{\rm{e}}^{2x}} \end{array} \right.\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiabg2 % da9maaeiaabaWaaSaaaeaacaaIXaaabaGaaGOmaaaacaWG4bGaaiOl % aiaabwgadaahaaWcbeqaaiaaikdacaWG4baaaaGccaGLiWoadaqhaa % WcbaGaaGimaaqaaiaaikdaaaGccqGHsisldaWcaaqaaiaaigdaaeaa % caaIYaaaamaapehabaGaaeyzamaaCaaaleqabaGaaGOmaiaadIhaaa % GccaqGKbGaamiEaaWcbaGaaGimaaqaaiaaikdaa0Gaey4kIipaaaa!4C27! I = \left. {\frac{1}{2}x.{{\rm{e}}^{2x}}} \right|_0^2 - \frac{1}{2}\int\limits_0^2 {{{\rm{e}}^{2x}}{\rm{d}}x} \)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Zaaq % GaaeaadaWcaaqaaiaaigdaaeaacaaIYaaaaiaadIhacaGGUaGaaeyz % amaaCaaaleqabaGaaGOmaiaadIhaaaaakiaawIa7amaaDaaaleaaca % aIWaaabaGaaGOmaaaakiabgkHiTmaaeiaabaWaaSaaaeaacaaIXaaa % baGaaGinaaaacaqGLbWaaWbaaSqabeaacaaIYaGaamiEaaaaaOGaay % jcSdWaa0baaSqaaiaaicdaaeaacaaIYaaaaaaa!48D1! = \left. {\frac{1}{2}x.{{\rm{e}}^{2x}}} \right|_0^2 - \left. {\frac{1}{4}{{\rm{e}}^{2x}}} \right|_0^2\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Jaae % yzamaaCaaaleqabaGaaGinaaaakiabgkHiTmaalaaabaGaaGymaaqa % aiaaisdaaaGaaeyzamaaCaaaleqabaGaaGinaaaakiabgUcaRmaala % aabaGaaGymaaqaaiaaisdaaaaaaa!3F94! = {{\rm{e}}^4} - \frac{1}{4}{{\rm{e}}^4} + \frac{1}{4}\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS % aaaeaacaaIZaGaaeyzamaaCaaaleqabaGaaGinaaaakiabgUcaRiaa % igdaaeaacaaI0aaaaaaa!3BFE! = \frac{{3{{\rm{e}}^4} + 1}}{4}\)