L = 1. 
fbut = ((4 (Sin[((π x)/L)]^2 + Sin[((2 π x)/L)]^2))/L)
Plot[fbut, {x, 0, L}]
fhex = ((4 (Sin[((π x)/L)]^2 + Sin[((2 π x)/L)]^2 + Sin[((3 π x)/L)]^2))/L)
Plot[fhex, {x, 0, L}]
fbenz = (6/L)
Plot[fbenz, {x, 0. , L}]
fbenzplus = 
      (2/L) + ((4 Sin[((2 π x)/L)]^2)/L) + ((2 Cos[((2 π x)/L)]^2)/L)
Plot[fbenzplus, {x, 0, L}]
fbenzmin = 
      (2/L) + ((4 Sin[((2 π x)/L)]^2)/L) + ((4 Cos[((2 π x)/L)]^2)/L) + ((2 Sin[((4 π x)/L)]^2)/L)
Plot[fbenzmin, {x, 0, L}]