$\int e^{x} \{f (x) + f' (x)\} d x =$

(a) e^x f (x) + C
(b) e^x + f (x)
(c) 2e^x f (x)
(d) e^x − f (x)

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Solution

(a) e^x f (x) + C

$Let I = \int e^{x} \{f (x) + f' (x)\} d x Putting e^{x} f (x) = t \Rightarrow [e^{x} \cdot f (x) + e^{x} f' (x)] d x = d t ∴ I = \int d t = t + C = e^{x} f (x) + C [∵ t = e^{x} f (x)]$

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