int 3^x left(f^{prime}(x) + f(x) log 3right) | vedclass

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(C) Let $I = \int 3^x \left(f^{\prime}(x) + f(x) \log 3\right) dx$. We can rewrite the integrand as: $I = \int \left(3^x f^{\prime}(x) + 3^x f(x) \log

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$3^x f(x) + c$

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(C) Let $I = \int 3^x \left(f^{\prime}(x) + f(x) \log 3\right) dx$. We can rewrite the integrand as: $I = \int \left(3^x f^{\prime}(x) + 3^x f(x) \log 3\right) dx$. Recall the product rule for differentiation: $\frac{d}{dx} \left(3^x f(x)\right) = 3^x f^{\prime}(x) + f(x) \cdot \frac{d}{dx}(3^x) = 3^x f^{\prime}(x) + f(x) \cdot 3^x \log 3$. Thus,the integrand is the derivative of $3^x f(x)$. Therefore,$\int \frac{d}{dx} \left(3^x f(x)\right) dx = 3^x f(x) + c$.

$\int 3^x \left(f^{\prime}(x) + f(x) \log 3\right) dx$ is equal to

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