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**Abbas** Use a comparison to determine whether the integral converges or diverges:

A $\displaystyle \int \frac{x^2e^x}{lnx}dx = $ from 2 to infinite

This integral diverges , but how can I show that using the comparison test?

We have $\displaystyle \frac{x^2e^x}{\ln x}\geq e^x$ and clearly $\displaystyle \int\limits_2^\infty e^x\,dx$ diverges.

B $\displaystyle \int \frac{1000}{pi^(2x)+x^2}dx = $

What are the limits here?? $\displaystyle \frac{1000}{\pi^2x+x^2}\le \frac{1000}{x^2}$ , and $\displaystyle \int\limits_1^\infty \frac{1000}{x^2}\,dx =\lim_{b\to \infty}-\frac{1000}{b}+1000=1000$ , so the integral converges (unless the lower limit is not 1 but something else...)

Tonio

it is pi^2x in the denomenator