Question

\( \int e^x [f(x) + f'(x)] dx \)= \(\underline{\hspace{2cm}}\)

Hint:

When the integrand is of the form \( e^x \left[ f(x) + f'(x) \right] \), use the reverse product rule to simplify.

Answer 1

Step 1: Apply the product rule.
Using the product rule of differentiation in reverse, we get: \[ \int e^x [f(x) + f'(x)] dx = e^x [f(x)] + C. \]

Step 2: Conclusion.
Thus, \( \int e^x [f(x) + f'(x)] dx = e^x [f(x)] + C \).