The last boxed answer shown is:

$\int \sin^3(x)e^{\cos(x)}dx = (\cos^2(x) - 2\cos(x) + 1)e^{\cos(x)} + C$

Let me know if you need further clarification or a step-by-step explanation!

Here are some related questions you may find helpful:

1. How does integration by parts work in solving integrals like this?
2. Can you explain how substitution helps simplify these problems?
3. What is the general process for integrating functions involving exponential and trigonometric terms?
4. Could you show the intermediate steps leading to this boxed answer?
5. What are some other common integrals involving $\sin(x)$ and $\cos(x)$?

Tip: Always verify your steps in substitution and integration by parts to avoid errors in sign or constants!