## Calculus (3rd Edition)

The integral $\int_{5}^{\infty} \dfrac{dx}{x^2 \ln x}$ converges as well.
We are given the function $f(x)=\int_{5}^{\infty} \dfrac{dx}{x^2 \ln x}$ Since, $x \gt 5$ and $x^2 \gt 0$ $\dfrac{1}{x^2 \ln x} \lt \dfrac{1}{x^2}$ But the integral $\int_{5}^{\infty} \dfrac{dx}{x^2}$ shows a p-type integral with $2 \gt 1$. Thus, the integral $\int_{5}^{\infty} \dfrac{dx}{x^2}$ converges. Therefore, by the comparison test, the integral $\int_{5}^{\infty} \dfrac{dx}{x^2 \ln x}$ converges as well.