Answer
The integral converges to $19$.
Work Step by Step
Recall the convergence/divergence rules for "p-integrals" on page 439.
Since $ p= \frac{20}{19}>1$, the integral converges.
$$\int_1^\infty \frac{dx}{x^{20/19}}=\lim\limits_{R \to \infty}\int_1^R\frac{dx}{x^{20/19}}\\=\lim\limits_{R \to \infty} \frac{1}{-1/19}x^{-1/19}|_1^R=-19\lim\limits_{R \to \infty}(\frac{1}{R^{1/19}}-1)=19.$$
