1. Compute the area of the figure bounded on the plane Oxy by the lines $x=2, x=3, y=0, y=x^{2 / \ln x}$.
Answer: $e^{2}$.

Solution. Note that $\ln \left(x^{1 / \ln x}\right)=2$. Therefore, $x^{1 / \ln x}=e^{2}$ for permissible values of the variable $x$. Thus, the figure represents a rectangle of size $1 \times e^{2}$.

Evaluation. 11 points for the correct solution.