Si escogemos que la exponencial sea u, este factor se mantendr siempre en la integral y, adems, el monomio la potencia ser dv e iremos aumentando su grado al calcular v. SOLUCIN En este ejemplo no importa cules son los factores u y dv, ya que al integrar y al derivar e-x obtenemos -e-x y al integrar y al derivar cos x obtenemos sin x. Se trata de una integral cclica en la que tendremos que aplicar dos veces integracin por partes con la misma eleccin para no volver al paso anterior y tendremos que despejar la integral de la expresin obtenida. SOLUCIN Tenemos de nuevo una exponencial por un seno, por tanto, se trata de una integral cclica ya que tendremos que aplicar dos veces integracin por partes con la misma eleccin para no volver al paso anterior y despejar la integral de la expresin obtenida. Podemos escoger u y dv al azar. SOLUCIN Escogeremos el polinomio como u para reducir los exponentes hasta que desaparezcan SOLUCIN Cada vez que derivamos a integramos la exponencial obtenemos la misma exponencial pero multiplicada por una constante o la inversa de dicha constante , por lo que no nos importa si es u dv.

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