f(x) = 1 - 2e^(-x/N) + e^(-2x/N)

integ(f(x)) = integ( 1 - 2e^(-x/N) + e^(-2x/N) )
            = integ( 1 ) - 2*(integ(e^(-x/N))) + integ(e^(-2x/N))

since:
integ(1) = x + C
integ(e^(bx)) = (1/b)e^(bx) + C

integ(f(x)) = [ x+C ] + [ (-2N)e^(-x/N) + C ] + [ (-N/2)e^(-2x/N) + C ]