## Calculus (3rd Edition)

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