# Thread: Imporper Integrals divergence convergence

1. ## Imporper Integrals divergence convergence

Integral of:
dx / sqrt (x^4 + 4x^3) from upper limit b=1 and a=0

Does this integral converge or diverge from the work i did am thinking that it divergers, help someone confirom or show me how it worked!!
I poseted a simliar thread before same question but with different limits of integration, any help would be appreciated.

2. If it's hard to find an inequality for $0\le x\le1,$ you may try the following:

Put $x=\frac1u$ and the integral becomes $\int_{1}^{\infty }{\frac{dx}{\sqrt{1+4x}}}\ge \int_{1}^{\infty }{\frac{dx}{\sqrt{5x+4x}}}=\int_{1}^{\infty }{\frac{dx}{3\sqrt{x}}},$ which is clearly divergent.

3. I dont quite understand what u did? what happened to my orginal function?
dx / sqrt (x^4 + 4x^3), can you please tell me the process, and the letting x=1/u am not sure, thanks