El objetivo de emplear esta fórmula es simplificar el cálculo de una integral mediante la obtención de otras integrales más sencillas.

Si se quiere resolver una integral por partes, se debe descomponer el integrando en un producto de dos factores u y dv, elegidos convenientemente, luego se debe integrar dv para obtener v y finalmente aplicar la fórmula.

E J E M P L O S

∫ x e x dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaWG4bGaamyzamaaCaaaleqabaGaamiEaaaakiaadsgacaWG4baaleqabeqdcqGHRiI8aaaa@3CEA@ u=x MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDaiabg2da9iaadIhaaaa@38EB@ ,   dv= e x dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadAhacqGH9aqpcaWGLbWaaWbaaSqabeaacaWG4baaaOGaamizaiaadIhaaaa@3CDC@ du=dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadwhacqGH9aqpcaWGKbGaamiEaaaa@3ABD@ ,   v= ∫ e x dx= e x MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODaiabg2da9maapeaabaGaamyzamaaCaaaleqabaGaamiEaaaakiaadsgacaWG4bGaeyypa0JaamyzamaaCaaaleqabaGaamiEaaaaaeqabeqdcqGHRiI8aaaa@40FD@ Aplicando la fórmula:   ∫ x e x dx =x e x − ∫ e x dx=x e x − e x +K MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaWG4bGaamyzamaaCaaaleqabaGaamiEaaaakiaadsgacaWG4baaleqabeqdcqGHRiI8aOGaeyypa0JaamiEaiaadwgadaahaaWcbeqaaiaadIhaaaGccqGHsisldaWdbaqaaiaadwgadaahaaWcbeqaaiaadIhaaaGccaWGKbGaamiEaiabg2da9iaadIhacaWGLbWaaWbaaSqabeaacaWG4baaaOGaeyOeI0IaamyzamaaCaaaleqabaGaamiEaaaakiabgUcaRiaadUeaaSqabeqaniabgUIiYdaaaa@50DF@

I= ∫ (2x+3) cos⁡(−2x+7) dx u=2x+3  dv=cos⁡(−2x+7) dx du=2 dx  v= ∫ cos⁡(−2x+7) dx= sen(−2x+7) -2 I=(2x+3) sen(−2x+7) -2 − ∫ sen(−2x+7) -2 2 dx I=−(2x+3) sen(−2x+7) 2 + cos⁡(−2x+7) 2  + K MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYdf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=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@C4D5@

Algunos casos típicos de integración por partes Un polinomio P n MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBaaaleaacaWGUbaabeaaaaa@37E2@ , de grado n, por una función exponencial    ∫ P n (x)   e x  dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaWGqbWaaSbaaSqaaiaad6gaaeqaaOGaaiikaiaadIhacaGGPaaccaGae8hiaaIaamyzamaaCaaaleqabaGaamiEaaaakiaadsgacaWG4baaleqabeqdcqGHRiI8aaaa@4110@ ,   u= P n (x) MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDaiabg2da9iaadcfadaWgaaWcbaGaamOBaaqabaGccaGGOaGaamiEaiaacMcaaaa@3C42@ ,   dv= e x  dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadAhacqGH9aqpcaWGLbWaaWbaaSqabeaacaWG4baaaOGaamizaiaadIhaaaa@3CDC@   Repetir n veces. Un polinomio P n MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBaaaleaacaWGUbaabeaaaaa@37E2@ , de grado n, por una función seno o coseno    ∫ P n (x) sin⁡x  dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaWGqbWaaSbaaSqaaiaad6gaaeqaaOGaaiikaiaadIhacaGGPaGaci4CaiaacMgacaGGUbGaamiEaGGaaiab=bcaGiaadsgacaWG4baaleqabeqdcqGHRiI8aaaa@42C7@ ,  u= P n (x) MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDaiabg2da9iaadcfadaWgaaWcbaGaamOBaaqabaGccaGGOaGaamiEaiaacMcaaaa@3C42@ ,  dv=sin⁡x dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadAhacqGH9aqpciGGZbGaaiyAaiaac6gacaWG4bGaamizaiaadIhaaaa@3E93@    ∫ P n (x) cos⁡x  dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaWGqbWaaSbaaSqaaiaad6gaaeqaaOGaaiikaiaadIhacaGGPaGaci4yaiaac+gacaGGZbGaamiEaGGaaiab=bcaGiaadsgacaWG4baaleqabeqdcqGHRiI8aaaa@42C2@ ,  u= P n (x) MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDaiabg2da9iaadcfadaWgaaWcbaGaamOBaaqabaGccaGGOaGaamiEaiaacMcaaaa@3C42@ ,  dv=cos⁡x  dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadAhacqGH9aqpciGGJbGaai4BaiaacohacaWG4baccaGae8hiaaIaamizaiaadIhaaaa@3F5D@   Repetir n veces. Un polinomio P n MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBaaaleaacaWGUbaabeaaaaa@37E2@ , de grado n, por la función logaritmo    ∫ P n (x) ln⁡x  dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaWGqbWaaSbaaSqaaiaad6gaaeqaaOGaaiikaiaadIhacaGGPaGaciiBaiaac6gacaWG4baccaGae8hiaaIaamizaiaadIhaaSqabeqaniabgUIiYdaaaa@41D3@ ,   u=ln⁡x MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDaiabg2da9iGacYgacaGGUbGaamiEaaaa@3ACF@ ,   dv= P n (x)  dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadAhacqGH9aqpcaWGqbWaaSbaaSqaaiaad6gaaeqaaOGaaiikaiaadIhacaGGPaaccaGae8hiaaIaamizaiaadIhaaaa@3FE1@ Una potencia del logaritmo    ∫ (ln⁡x) m dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaGGOaGaciiBaiaac6gacaWG4bGaaiykamaaCaaaleqabaGaamyBaaaakiaadsgacaWG4baaleqabeqdcqGHRiI8aaaa@3F32@ ,  u= (ln⁡x) m MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDaiabg2da9iaacIcaciGGSbGaaiOBaiaadIhacaGGPaWaaWbaaSqabeaacaWGTbaaaaaa@3D47@ ,  dv= dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadAhacqGH9aqpcaWGKbGaamiEaaaa@3ABE@ Una función exponencial por una función seno o coseno    ∫ e x sin⁡x  dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaWGLbWaaWbaaSqabeaacaWG4baaaOGaci4CaiaacMgacaGGUbGaamiEaGGaaiab=bcaGiaadsgacaWG4baaleqabeqdcqGHRiI8aaaa@4091@ ,  u= e x MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDaiabg2da9iaadwgadaahaaWcbeqaaiaadIhaaaaaaa@3A02@ ,  dv=sin⁡x dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadAhacqGH9aqpciGGZbGaaiyAaiaac6gacaWG4bGaamizaiaadIhaaaa@3E93@    ∫ e x cos⁡x  dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qaaeaacaWGqbWaaSbaaSqaaiaad6gaaeqaaOGaaiikaiaadIhacaGGPaGaci4yaiaac+gacaGGZbGaamiEaGGaaiab=bcaGiaadsgacaWG4baaleqabeqdcqGHRiI8aaaa@42C2@ ,  u= e x MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDaiabg2da9iaadwgadaahaaWcbeqaaiaadIhaaaaaaa@3A02@ ,  dv=cos⁡x  dx MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadAhacqGH9aqpciGGJbGaai4BaiaacohacaWG4baccaGae8hiaaIaamizaiaadIhaaaa@3F5D@    Hacer dos veces y despejar la integral.

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