Question

If $g\left(x\right)=\int x^x{\log }_e\left(ex\right)dx$ then $g\left(\pi \right)$ equals

• A. $\pi {\log }_e\pi$
• B. ${\pi }^{\pi }{\log }_e(e\pi )$
• C. ${\pi }^{\pi }{\log }_e(\pi )$
• D. ${\pi }^{\pi }$

Answer 1

The correct option is D ${\pi }^{\pi }$

$\begin{array}{c}g\left(x\right)={\int }^{}{x}^x\left(1+\log e^x\right)dx\\ ={\int }^{}d\left(x^x\right)\\ g\left(x\right)=x^x\\ g\left(\pi \right)={\pi }^{\pi }\end{array}$