# Integration: Convergence/Divergence Tests

by WaterPoloGoat
Tags: integration, tests
 P: 14 Does anyone know of helpful tests that can help me determine whether an improper integral converges or diverges? Specifically ones where you don't have to solve the integral? For example, the problem I'm solving has a very complicated solution to the integral: the problem: integrate dx/(sqrt(x+x^3)) from 0 to $$\infty$$. I have tried integrating, and ended up using Maple, only to get a very complicated answer. But I only need to prove whether it converges or diverges. That's it. Any ideas?
 HW Helper P: 3,307 Integration: Convergence/Divergence Tests i meant use the property of integrals $$\int_a^b dx \frac{1}{\sqrt{x^3+x}} = \int_a^c dx \frac{1}{\sqrt{x^3+x}} + \int_c^b dx \frac{1}{\sqrt{x^3+x}}$$ then if you pick c correctly, your approach should work for the 2nd part, but you'll have to think about the 1st... maybe consider a variable change