# Obtain integral result without assumptions

I have the following two functions:

a[x_] : = w & # 39; & # 39;[x]^ 2
second[x_] : = 1 / L * !  (
* SubsuperscriptBox[([Integral]),  ( (- L ) / 2 ),  (L / 2 )] (one /
2   (w & # 39; )[x]^ 2 [DifferentialD]X ) )

Then I calculate:

1/2 * !  (
* SubsuperscriptBox[([Integral]),  ( (- H ) / 2 ),  (H / 2 )] (
* SubsuperscriptBox[([Integral]),  ( (- W ) / 2 ),  (W / 2 )] (
* SubsuperscriptBox[([Integral]),  ( (- L ) / 2 ),  (L / 2 )] * SubscriptBox[([Sigma]),  (0 )] (( (- z )  * a[x] +
second[x]) )  [DifferentialD]X  [DifferentialD]Y
[DifferentialD]z ) ) ) + Y / 2 * !  (
* SubsuperscriptBox[([Integral]),  ( (- H ) / 2 ),  (H / 2 )] (
* SubsuperscriptBox[([Integral]),  ( (- W ) / 2 ),  (W / 2 )] (
* SubsuperscriptBox[([Integral]),  ( (- L ) / 2 ),  (L / 2 )] * SuperscriptBox[(((-z)*a[(((-z)*a[(((-z)*a[(((-z)*a[x] +
second[x]) ),  (two )][DifferentialD]X  [DifferentialD]Y   ( (
[DifferentialD])  (z )  (\) ) ) ) )

The result is this:

(1 / (2 L)) H W Integrate[1/2 Derivative[1][w][x]^ 2, {x, - (L / 2), L / 2},
Assumptions -> (- (H / 2) <z < H/2 || -(H/2) > z> H / 2) && (- (W / 2) <
Y < W/2 || -(W/2) > y> W / 2) && (Im[L] ! = 0 || - (L / 2) <x <L /
2 || L / 2 <x < -(L/2))] Subscript[[Sigma], 0] +
1/2 Y ((1/(L^2))
H W Integrate[1/2 Derivative[1][w][x]^2, {x, -(L/2), L/2},
Assumptions -> (- (H / 2) <z < H/2 || -(H/2) > z> H /
2) && (- (W / 2) <and < W/2 || -(W/2) > y> W / 2) && (Im[L] ! =
0 || - (L / 2) <x <L / 2 || L / 2 <x <- (L / 2))]^ 2 +
1/12 H ^ 3 W (w ^ [Prime][Prime])[x]^ 4)

How can I get this result with all those assumptions?
All the variables are real and positive.