Answer
The integral $\int_{0}^{1} \dfrac{e^x}{x^2}\ dx$ diverges.
Work Step by Step
We are given the function
$f(x)=\int_{0}^{1} \dfrac{e^x}{x^2} \ dx$
Since, $e^x \gt 1$
This yields:
$\dfrac{e^x}{x^2} \gt \dfrac{1}{x^2} $
We know that the integral $\int_{0}^{1} \dfrac{dx}{ x^2}$ diverges because $2 \gt 1$.
Therefore, by the comparison test, the integral $\int_{0}^{1} \dfrac{e^x}{x^2}\ dx$ diverges as well.
