from scipy.special import erf
import math
import numpy as np
import matplotlib.pyplot as plt
import scipy.integrate as integrate
import scipy.special as special
def e(x):
    return math.exp(x)


#Defines the PDF
def pdf(x):
    f= (np.sin(6*x)**2+3*np.cos(x)**2*np.sin(4*x)**2+1)*np.exp(-x**2/2)
    mass=(-4-3*e(22)-6*e(40)-3*e(54)+6*e(70)+18*e(72))*math.sqrt(math.pi*0.5)/(4*e(72))
    return f/mass;
#Computes the CDF
def cdf(x):
    f=integrate.quad(pdf, -10, x)[0]
    return f