$\int_0^\infty \frac{ x^{1/3}}{(x+a)(x+b)} dx $ $$\int_0^\infty \frac{ x^{1/3}}{(x+a)(x+b)} dx$$ where $a>b>0$
What shall I do?
I have diffucty when I meet multi value function.

You may first use $x=t^3$ and $dx=3t^2dt$, and then make the integral as the sum of two integral using the following:
$$ \frac{ 3t^3}{(t^3+a)(t^3+b)} = \frac{ \frac{-3a}{b-a}}{(t^3+a)}+ \frac{ \frac{3b}{b-a}}{(t^3+b)}$$
