\( \int e^x [f(x) + f'(x)] dx \)= \(\underline{\hspace{2cm}}\)
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Solution and Explanation
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, \( \int e^x [f(x) + f'(x)] dx = e^x [f(x)] + C \).
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