# calculus and analysis – Evaluating a 2d integral

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?