$\int e^{x}\big[f(x)+f'(x)\big]\,dx$ equals

Question

Accepted Answer

C. $e^{x}f(x)+C$

1. Split into $\int e^{x}f(x)\,dx+\int e^{x}f'(x)\,dx$.
2. Integrate $\int e^{x}f(x)\,dx$ by parts: $e^{x}f(x)-\int e^{x}f'(x)\,dx$.
3. Adding back $\int e^{x}f'(x)\,dx$, the two integral terms cancel.
4. Result: $e^{x}f(x)+C$.
_Source: syllabus Mathematics Ch 7 "Integrals", p.328_

Answer

$e^{x}f'(x)+C$

Answer

$f(x)+f'(x)+C$

Answer

$e^{x}\big[f(x)-f'(x)\big]+C$

$\int e^{x}\big[f(x)+f'(x)\big]\,dx$ equals

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