Evaluate \(\int_{0}^{1} 3^{\prime} \log 3 d x\).
Explanation
\begin{array}{l}
\text { To evaluate } \begin{aligned}
\int_{0}^{1} 3^{\prime} \log 3 d x \\
\text { let } y &=3^{x} \\
\frac{d y}{d x} &=3^{\prime} \log _{c} 3 \\
d x &=\frac{d y}{3^{\prime} \log 3} \\
\Rightarrow \int_{0}^{1} 3^{\prime} \log 3 d x &=\int_{0}^{1} 3^{\prime} \log 3 \cdot \frac{d y}{3^{\prime} \log 3} \\
&=\int_{0}^{1} d y=[y]_{0}^{1} \\
\text { but } y=3^{x} \\
=\left.3^{\prime}\right|_{0} ^{1}=31-30=3-1=2
\end{aligned}
\end{array}