# problems with integration of an equation

I am trying to integrate the following. I assumed some kind of analytical method is required but I have no idea how.

$0.5*b\intop_{-1}^{1}\frac{x\left[(a-x)g_{1}+(a+x)g_{2}\right]^{2}}{\left[(a-x)z_{1}+(a+x)z_{2}\right]}dx$,

where $a$ and $b$ are constants and

$g = b*((a-x)g_1 +(a+x) g_2$

$z = b*((a-x)z_1 + (a+x)z_2$

and and $g$, $g1$, $g2$, $f1$, $f2$ and $x$ are variables.The answer would need to be in terms of $g1$, $g2$, $f1$, $f2$.