Why can't a value for this definite integral be found? I was trying to find out if  $\int _0^{\infty }\:\frac{1}{\left(1+x^3\right)^{\frac{1}{2}}}dx$ converges or diverges. I split it into a sum, that is
$\int _0^{1 }\:\frac{1}{\left(1+x^3\right)^{\frac{1}{2}}}dx$ + $\int _1^{y }\:\frac{1}{\left(1+x^3\right)^{\frac{1}{2}}}dx$
where $y>1$ . I found that the second integral of the sum converges as y tends to infinity, but I can not evaluate the first integral. When I plot the graph, I can see clearly that the area under the curve of $f(x)=\frac{1}{\left(1+x^3\right)^{\frac{1}{2}}}$ with x in $[0,1]$ is finite. What is wrong with that integral?

Hint: Let $~t=\dfrac1{1+x^3}~$ and then recognize the expression of the beta function in the new integral.
