## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 441: 75

#### Answer

The integral $\int_{0}^{1} \dfrac{dx}{(xe^x+x^2)}$ diverges.

#### Work Step by Step

We are given the function $f(x)=\int_{0}^{1} \dfrac{dx}{(xe^x+x^2)}$ Since, $x(e^x+x) \leq x(e+1)$ This yields: $\dfrac{1}{x(e+1)} \leq \dfrac{1}{x(e^x+x)}$ But the integral $\int_{0}^{1} \dfrac{dx}{x(e+1)}$shows a p-type integral with $p=1$. Thus, the integral $\int_{0}^{1} \dfrac{dx}{x(e+1)}$ diverges. Therefore, by the comparison test, the integral $\int_{0}^{1} \dfrac{dx}{(xe^x+x^2)}$ diverges as well.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.