I have to use the comparison test to determine if the integral diverges or converges but I am confused about how to do this. Please help.
integral from 1 to infinity of dx/(square root(x^4 + 4x^3))
This was posted before, anyway, for $\displaystyle x\ge1$ it's $\displaystyle \frac{1}{\sqrt{{{x}^{4}}+4{{x}^{3}}}}\le \frac{1}{\sqrt{{{x}^{4}}}}=\frac{1}{{{x}^{2}}},$ so your integral converges by direct comparison with $\displaystyle \int_1^\infty\frac{dx}{x^2}.$