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

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

Evaluation. 11 points for a correct solution.