Hints

• Compute the vector field:
  F:= grad(1/sqrt(x^2+y^2), [x,y]); # F=grad(P)
• To compute F(g(t)), you need to replace x and y with their parametrizations:
  G:= subs(x=6+t, y=0, eval(F)); # compute F(g(t))
• To compute the inner product of F(g(t)) and g'(t), we use Maple's innerprod command:
  Q:= innerprod( G, diff([6+t,0], t) ); # F(g(t)).g'(t)
• The line integral is then
  evalf(Int(Q, t=0..1)); # integral of F(g(t)).g'(t)