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$\int 3^x\left(f^{\prime}(x)+f(x) \log 3\right) d x$ is equal to
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The correct answer is:
$3^x f(x)+c$
Let $\left.I=\int 3^x f^{\prime}(x)+f(x) \log 3\right) d x$
$I=\int 3^x f^{\prime}(x) d x+\int 3^x f(x) \log 3 d x$
$\begin{aligned} & I=3^x f(x)-\int\left(3^x f(x) \log 3\right) d x+\int 3^x f(x) \log 3 d x \\ & I=3^x f(x)+c\end{aligned}$
$I=\int 3^x f^{\prime}(x) d x+\int 3^x f(x) \log 3 d x$
$\begin{aligned} & I=3^x f(x)-\int\left(3^x f(x) \log 3\right) d x+\int 3^x f(x) \log 3 d x \\ & I=3^x f(x)+c\end{aligned}$
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