I would like to calculate this integral

begin{align*}

I(s_1,s_2,s_{12},m) =

int_{0}^{1} {rm d}x int_{0}^{1-x}

{rm d}y Big(

x y

Big(

y(1-y)s_1 + x(1-x)s_2 + 2 xy s_{12} -m^2

Big)^{-1}

Big),

end{align*}

where $s_{1}, s_{2}, s_{12}$ and $m$ are constant real values.

To evaluate this integral, I’ve used

```
$Assumptions = Element({s1, s2, s12, m}, Reals) && s1 >= 0 && s2 >= 0 && m > 0;
FullSimplify(
Integrate(Integrate(
x*y/(y*(1 - y)*s1 + x*(1 - x)*s2 + 2*x*y* s12 - m^2), {y, 0, 1 - x}), {x, 0, 1})) // Timing
```

This evaluation is very slow, and I wasn’t able to get the final result. Does anyone have a suggestion to speed up the calculation?