2 deleted 1 characters in body edited Feb 18 '14 at 2:46 Dr. belisarius 109k1111 gold badges173173 silver badges391391 bronze badges It's a bug, of course. Mathematica gets dizzy by the "hanging" integration order (I believe). As simple as it is, it was tough to find out, but it gives the right result if you just change the order of limits: $Assumptions = {ρ > 0, L > 0}; limits = Sequence[{ux, 0, L}, {uy, 0, ux}, {vx, 0, L}, {vy, 0, vx}]; (* instead of limits = Sequence[{ux, 0, L}, {vx, 0, L}, {uy, 0, ux}, {vy, 0, vx}] *) N1 = Integrate[a1 = Exp[-ρ (ux - uy) (vx - vy)], limits]; N2 = Integrate[a2 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy)), limits]; N3 = Integrate[a3 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy))^2, limits]; N4 = Integrate[a4 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy))^3, limits]; int1 = Integrate[4 ρ (a1 - 7/2 a2 + 2 a3 - 1/4 a4), limits] int2 = FullSimplify[4 ρ (N1 - 7/2 N2 + 2 N3 - 1/4 N4)] (* (1 - E^(-L^2 ρ)) L^2 (1 - E^(-L^2 ρ)) L^2 *)  It's a bug, of course. Mathematica gets dizzy by the "hanging" integration order (I believe). As simple as it is, it was tough to find out, but it gives the right result if you just change the order of limits: $Assumptions = {ρ > 0, L > 0}; limits = Sequence[{ux, 0, L}, {uy, 0, ux}, {vx, 0, L}, {vy, 0, vx}]; (* instead of limits = Sequence[{ux, 0, L}, {vx, 0, L}, {uy, 0, ux}, {vy, 0, vx}] *) N1 = Integrate[a1 = Exp[-ρ (ux - uy) (vx - vy)], limits]; N2 = Integrate[a2 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy)), limits]; N3 = Integrate[a3 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy))^2, limits]; N4 = Integrate[a4 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy))^3, limits]; int1 = Integrate[4 ρ (a1 - 7/2 a2 + 2 a3 - 1/4 a4), limits] int2 = FullSimplify[4 ρ (N1 - 7/2 N2 + 2 N3 - 1/4 N4)] (* (1 - E^(-L^2 ρ)) L^2 (1 - E^(-L^2 ρ)) L^2 *)  It's a bug, of course. Mathematica gets dizzy by the "hanging" integration order (I believe). As simple as it is, it was tough to find out but it gives the right result if you just change the order of limits: $Assumptions = {ρ > 0, L > 0}; limits = Sequence[{ux, 0, L}, {uy, 0, ux}, {vx, 0, L}, {vy, 0, vx}]; (* instead of limits = Sequence[{ux, 0, L}, {vx, 0, L}, {uy, 0, ux}, {vy, 0, vx}] *) N1 = Integrate[a1 = Exp[-ρ (ux - uy) (vx - vy)], limits]; N2 = Integrate[a2 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy)), limits]; N3 = Integrate[a3 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy))^2, limits]; N4 = Integrate[a4 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy))^3, limits]; int1 = Integrate[4 ρ (a1 - 7/2 a2 + 2 a3 - 1/4 a4), limits] int2 = FullSimplify[4 ρ (N1 - 7/2 N2 + 2 N3 - 1/4 N4)] (* (1 - E^(-L^2 ρ)) L^2 (1 - E^(-L^2 ρ)) L^2 *)  1 answered Feb 18 '14 at 2:28 Dr. belisarius 109k1111 gold badges173173 silver badges391391 bronze badges It's a bug, of course. Mathematica gets dizzy by the "hanging" integration order (I believe). As simple as it is, it was tough to find out, but it gives the right result if you just change the order of limits: $Assumptions = {ρ > 0, L > 0}; limits = Sequence[{ux, 0, L}, {uy, 0, ux}, {vx, 0, L}, {vy, 0, vx}]; (* instead of limits = Sequence[{ux, 0, L}, {vx, 0, L}, {uy, 0, ux}, {vy, 0, vx}] *) N1 = Integrate[a1 = Exp[-ρ (ux - uy) (vx - vy)], limits]; N2 = Integrate[a2 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy)), limits]; N3 = Integrate[a3 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy))^2, limits]; N4 = Integrate[a4 = Exp[-ρ (ux - uy) (vx - vy)] (ρ (ux - uy) (vx - vy))^3, limits]; int1 = Integrate[4 ρ (a1 - 7/2 a2 + 2 a3 - 1/4 a4), limits] int2 = FullSimplify[4 ρ (N1 - 7/2 N2 + 2 N3 - 1/4 N4)] (* (1 - E^(-L^2 ρ)) L^2 (1 - E^(-L^2 ρ)) L^2 *)