Integrate[(1/l)*E^((-c)*(r^2 + (l - r)^2)), {r, 0, l}]

P[x_]:=1-E^(-c*x^2)
P'

Integrate[2*c*l*E^(-c*l^2)*(((E^(-((c (l^2))/2))) (Sqrt[(π/2)]) Erf[(((Sqrt[c]) l)/(Sqrt[2]))])/((Sqrt[c]) l)),{l,0,Infinity}]