# Divergent or Convergent?

1. Mar 7, 2006

### Aki

I want to know if the integral

$$\int_0^{\infty} dx/(4x^3 + x^(1/3))$$

is convergent or divergent?

Thanks

Last edited: Mar 7, 2006
2. Mar 7, 2006

### shmoe

What have you tried? Have you compared it with integrals whose convergece/divergence you know? Keep in mind your integrand is also undefined at 0.

Use {} instead of () to group things in latex, click on $$\int_{0}^{\infty}$$

3. Mar 7, 2006

### Aki

Well I'm just not sure what happens when

$$\int_{0}^{1}dx/x^{1/3}$$

I think it converges, but I"m not too sure.
because when that function is below $$1/x$$ on the graph

Last edited: Mar 7, 2006
4. Mar 8, 2006

### HallsofIvy

Staff Emeritus
What is the anti-derivative of $\frac{1}{x^{\frac{1}{3}}}= x^{-\frac{1}{3}}$

Last edited: Mar 9, 2006
5. Mar 9, 2006

### dextercioby

Is the function $\frac{1}{4x^{3}+x^{1/3}}$ ? If so, what is its limit to $0^{+}$ ?

Daniel.