Numerical integration for a slow converging integral

Question

I basically have a problem with numerical integrations of this type:

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import quad

# Parameter
T = 94
Eps_inf = 3.05
Eps_s = 19.184544603857724
tau_0 = 1.27*10**-16
tau_CD = 0.34580390675331274
gamma = 0.49
C_pek = 1/Eps_inf - 1/Eps_s
hbar = 6.582119569*10**-16

# Functions
def func(w):
    return -4 * 1/(np.pi * C_pek) * Eps(w).imag/abs(Eps(w))**2

def Eps(w):
    return Eps_inf + (Eps_s - Eps_inf)/(1 + (1j * w * tau_CD))**gamma

w = np.logspace(-9,80,100000)
y = func(w)

IntegrandS = quad(lambda w: func(w),0,np.inf,limit=100000)[0]
print(f'quadResult: {IntegrandS}')

This gives me the warning: The integral is probably divergent, or slowly convergent.

And the function is indeed slowly converging:

If I put in the upper limit of the integration just a big numer like 1e15 it gives me a result but that result will never converge for higher and higher integration limits.

Is there anyway to treat this function, so that the quad function (or any other integration method, i also tried scipys trapz, giving me the same problem) can deal with this function?

Thanks!