calculus and analysis – How to integrate faster

I always wanted to know how to speed up my integral computation in Mathematica. Is there some techniques that i am unaware to make the integration faster.

Here an example:

func = (2 (μG2-μPi2) (5 x^2+5 x (z-2)-4 (η-ρ+z-1)))/mb^2-12 (x+z-2) (-η-ρ+x+z-1)

The integration is given as:

Integrate(func, {x, 2*Sqrt(η), 1 + η - ρ}, 
  {z, -((-(2*(η - ρ + Sqrt(x^2 - 4*η) - 1)) + x*(Sqrt(x^2 - 4*η) - 2) + x^2)/
     (Sqrt(x^2 - 4*η) + x - 2)), (2*(-η + ρ + Sqrt(x^2 - 4*η) + 1) - 
     x*(Sqrt(x^2 - 4*η) + 2) + x^2)/(Sqrt(x^2 - 4*η) - x + 2)}, 
  Assumptions -> {0 < ρ < 1, 0 < η < 1, ρ < η, η + 1 > 2*Sqrt(η) + ρ, 
    Element(mb, Reals)}, GenerateConditions -> False)

On my laptop i need 42.219 s to solve the integral. However, my integrals are getting more and more complicated so to learn new optimization methods would be much appreciated.