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Integration of "Which"


Hello, and thank you for your help .
This is as a follow up to my last question about integration of Which .
My problem is alittle more complicated:

W[i_, x_]:= Which[[i == 1,Which[0 <= x <=  1/2, 0, 1/2 <  x <=  1,2(x - 1)],
         i == 2,Which[0 <=  x <=  1/2, 2x, 1/2 <  x <=  1, 2(1 - x)]
         i == 3,Which[0 <=  x <=\ 1/2, 1 - 2x, 1/2 <  x <= 1,0 ]];
k[x_] := 1 + x;

K[i_, j_, x_] := 
  N[-(Integrate[D[W[j, x], x]*
       D[W[i, x], x]*k[x], 
      {x, 0, 1/2}] + 
     Integrate[D[W[j, x], x]*
       D[W[i, x], x]*k[x], 
      {x, 1/2, 1}])]
so I can`t use UnitStep , maybe ramp will work?
Anyway I can`t integrate this , is there a way to solve this ?


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