import scipy.integrate
import numpy as np

alpha = -0.5
f = lambda n : scipy.integrate.quad(lambda x: np.abs(x)**alpha * np.cos(n*x),-np.pi,np.pi,points=[0])[0]

x = np.arange(10,100)
y = np.array([f(i) for i in x])

print np.polyfit(np.log(x),np.log(np.abs(y)),1)