para = h -> (E^(-s))

example 7.4  p.150

badP = 17 - (∫_0^1) 30 \[DifferentialD]x + 13

badM = +(∫_0^1) 30 x \[DifferentialD]x + 24 - 
        13 3

fs1 = 17 - 30/s (1 - h) + 24 s h^2 + 13 h^3 /. para

ex ample 7.5 p.151

badP = 
      120 - (∫_1^2) 300 \[DifferentialD]x + 80 + 100

badM = -90 + (∫_1^2) 300 x \[DifferentialD]x - 80 2 + 
        200 - 100 4

fs2 = -90 s + 120 - 300/s (h - h^2) + 80 h^2 + 200 s h^3 + 
          100 h^4 /. para

ex ample 7.6  p.153

qs = Expand[fs1/s]
qx = InverseLaplaceTransform[qs, s, x]
% /. x ->  3

ms = qs/s;
mx = InverseLaplaceTransform[ms, s, x]
% /. x ->  3

Plot[{qx, mx}, {x, 0, 3}, PlotRange ->  {-15, 20}, 
      PlotStyle ->  {Hue[0.9], Hue[0.7]}, 
      AspectRatio ->  0.3]

example 7.7  p.154

qs = Expand[fs2/s]
qx = InverseLaplaceTransform[qs, s, x]
% /. x ->  4

ms = qs/s;
mx = InverseLaplaceTransform[ms, s, x]
% /. x ->  4

Plot[{qx, mx}, {x, 0, 4}, PlotRange ->  {-200, 150}, 
      PlotStyle ->  {Hue[0.9], Hue[0.7]}, 
      AspectRatio ->  0.3]