Convergence of Integral with Divergent Function at 0+

[Aki]

I want to know if the integral

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

is convergent or divergent?Thanks

 

[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 $$\int_{0}^{\infty}$$

 

[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

 

[HallsofIvy]

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

 

[dextercioby]

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

Daniel.