Solve the triple integral( xyz*e^(-x^2-2y^2-4z^2)dxdydz) where the bounds are x: 0...12, y: 0...12, z: 0...8

∫(x = 0 to 12) ∫(y = 0 to 12) ∫(z = 0 to 8) xyz e^(-x^2 - 2y^2 - 4z^2) dz dy dx
= ∫(x = 0 to 12) xe^(-x^2) dx * ∫(y = 0 to 12) ye^(-2y^2) dy * ∫(z = 0 to 8) ze^(-4z^2) dz
= (-1/2)e^(-x^2) {for x = 0 to 12} * (-1/4)e^(-2y^2) {for y = 0 to 12} * (-1/8)e^(-4z^2) {for z = 0 to 8}
= (1/64) (1 - e^(-144)) (1 - e^(-288)) (1 - e^(-256)).

I hope this helps!