The integral \( \int \frac{x + 5}{(x + 6)^2} e^x \, dx \) can be simplified using substitution. Let $u = x + 6$, implying $du = dx$ and $x = u - 6$. The integral transforms to \( \int \frac{(u - 6) + 5}{u^2} e^{u - 6} \, du \), which simplifies to \( \int \frac{u - 1}{u^2} e^{u - 6} \, du \). This can be decomposed into \( \int \frac{1}{u} e^{u - 6} \, du - \int \frac{1}{u^2} e^{u - 6} \, du \). The first term evaluates to $\frac{e^{u-6}}{u}$. The second term, requiring integration by parts or identification of a standard form, yields \( \frac{e^x}{x + 6} + C \).