$\int 2^{x} (f^{'} (x) + f (x) log 2) d x$ is

2^{x} f^{'} (x) + C

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2^{x} f (x) + C

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2^{x} (log 2) f (x) + C

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(log 2) f (x) + C

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Solution

The correct option is A $2^{x} f (x) + C$
Let $I = \int 2^{x} (f^{'} (x) + f (x) log 2) d x$
$= \int 2^{x} f^{'} (x) d x + \int 2^{x} f (x) d x log 2 d x$
$= 2^{x} f (x) + C$

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