Example 2.23. $\int_{1}^{\infty} \frac{d x}{x^{3 / 2}}$.
Solution. By the definition of the improper integral with an infinite upper limit

$$
\int_{1}^{\infty} \frac{d x}{x^{3 / 2}}=\lim _{b \rightarrow \infty} \int_{1}^{b} \frac{d x}{x^{3 / 2}}=\left.\lim _{b \rightarrow \infty}\left(-\frac{1}{2 x^{1 / 2}}\right)\right|_{1} ^{b}=\frac{1}{2}
$$