# Math Help - comparison theroem

1. ## comparison theroem

Hi the instructions are to use the comparison thereom to determine whether the following integral is convergent or divergent

integral sign (S) sqrt x/(x^3 +1) dx

I am running into a mental road block and can't figure out how to get rid of the sq rt x as the numerator

What do I need to do to simplify this integral?

Thanks

Struggling calculus beginner

2. i see no bounds, but well.

i'll presume that is $0\le x<\infty$ or $1\le x<\infty.$

suppose is the first case, the split the integral into two pieces, one goes for $[0,1]$ and let's analyze the second piece for $x\ge1,$ then $\frac{\sqrt{x}}{x^{3}+1}<\frac{\sqrt{x}}{x^{3}}=\f rac{1}{x^{5/4}},$ hence the integral converges.