```
Integrate[
 Boole[{ -2 <= 2 x + 7 y <= 2 && -2 <= 3 x + 6 y <= 2}](6 x^2 + 
    33 x*y + 42 y^2)^4, {x, -∞, ∞}, {y, -∞, ∞}]
```
> `4096/225`

```
Integrate[(6 x^2 + 33 x*y + 42 y^2)^4, {x, y} ∈ 
  ImplicitRegion[{ -2 <= 2 x + 7 y <= 2 && -2 <= 3 x + 6 y <= 2}, {x, 
    y}]]
```
> `4096/225`

```
sol = Solve[{u == 2 x + 7 y, v == 3 x + 6 y}, {x, y}][[1]];
jacobian = 
  With[{u = 2 x + 7 y, v = 3 x + 6 y}, Grad[{u, v}, {x, y}]] // Det //
    Abs;
Integrate[((6 x^2 + 33 x*y + 42 y^2)^4 /. sol)*1/jacobian, {u, -2, 
  2}, {v, -2, 2}]
```
> `4096/225`