Chapter 7.8, Problem 56ES

Use the results in Exercise 52.

In each part, use Exercise 52 to determine whether the integral converges or diverges. If it converges, then use part (b) of that exercise to find an upper bound on the value of the integral.

$\begin{array}{l}\text{(a)}{\displaystyle {\int }_2^{+\infty }\frac{\sqrt{x^3+1}}{x}dx}\\ \left(\text{b}\right){\displaystyle {\int }_2^{+\infty }\frac{x}{x^5+1}}dx\\ \left(\text{c}\right){\displaystyle {\int }_0^{+\infty }\frac{x{e}^x}{2x+1}dx}\end{array}$