# Prove convergence of improper integral of hard to factor denominator

I am trying to determine whether $$\int_{-3}^{2} \frac{xdx}{x^3+2x+2}\,.$$ converges or diverges

Usually, for improper integrals where there is a vertical asymptote, I try to split the integral up around the asymptote, but I can't really do that here cause I cannot factor it. Any recommendations?

Thanks

• This integral does not converge on the given interval – Dr. Sonnhard Graubner Nov 4 '18 at 18:34
• How would I actually go about proving that? I thought the same thing when I looked at the graph. – Flyrom Nov 4 '18 at 18:39

Hint: The denominator is positive at $$0$$ and negative at $$-1,$$ hence must be $$0$$ somewhere in between.