Ans: (C)
\(\int 2^{x}\left(f^{\prime}(x)+f(x) \log 2\right) d x=I\)
$$
\begin{aligned}
&\text { Let } g(x)=2^{x} f(x) \\
&\begin{aligned}
\Rightarrow g^{\prime}(x) &=2^{x} f^{\prime}(x)+2^{x} f(x) \log 2 \\
&=2^{x}\left(f^{\prime}(x)+f(x) \log 2\right)
\end{aligned} \\
&\therefore I=\int g^{\prime}(x) d x=g(x)+c=2^{x} f(x)+c
\end{aligned}
$$
