Questions: Resolver la siguiente integral I = ∫ cos^2(x) sen(x) dx

To solve the integral \(\int \cos^2(x) \sin(x) \, dx\), we can use a substitution method. Let \( u = \cos(x) \), then \( du = -\sin(x) \, dx \). This substitution simplifies the integral to a form that is easier to integrate.

Para resolver la integral \(\int \cos^2(x) \sin(x) \, dx\), realizamos la sustitución \(u = \cos(x)\). Entonces, \(du = -\sin(x) \, dx\), lo que implica que \(-du = \sin(x) \, dx\). Esto transforma la integral en:

\[ \int \cos^2(x) \sin(x) \, dx = -\int u^2 \, du \]

Ahora, integramos \(-\int u^2 \, du\):

\[ -\int u^2 \, du = -\frac{u^3}{3} + C \]

Sustituyendo de nuevo \(u = \cos(x)\), obtenemos:

\[ -\frac{\cos^3(x)}{3} + C \]

La solución de la integral es:

\[ \boxed{-\frac{\cos^3(x)}{3} + C} \]