def f(x):
    return 1/x

def integrale(a,b,dx):
    x = a
    somme = 0
    if b >= a :
        while x < b :
            somme = somme + f(x)*dx
            x = x + dx
    elif b < a :
        dx = - dx
        while x > b :
            somme = somme + f(x)*dx
            x = x + dx
    return somme


def ln(x) :
    dx = 0.000001
    y = integrale(1,x,dx)
    return y