I have this integral :

$$ {J}=\int\_{-1}^{+1}\frac{(1-x)^{-\frac{2}{3}}(1+x)^{-\frac{1}{3}}}{4+x^2}\,dx$$

There are three branch points for this integral : $1,-i,+i$ and two pole points $-2i$ and $+2i$ which lie outside. So can we say that there are no pole points for this integral and how to solve it.