将函数与 sympy.integrate 集成

如何解决将函数与 sympy.integrate 集成

我正在使用拉格朗日多项式逼近积分。我已正确设置多项式，但在最后一步中遇到了一些问题：

import numpy as np
from matplotlib import pyplot as plt
from matplotlib import axes as ax
import sympy
####Pyplot font settings

nvect = np.array([5,15,30,50])
#Left and right bounds of interploation points
xl = -5; xr=5;
xs = sympy.Symbol('X')

fcn = 1/(1+xs**2) # to be integrated from -5 to 5
int_exact = sympy.integrate(fcn,(xs,xl,xr))

f = sympy.lambdify(xs,fcn)

#Error vector
err = np.zeros(len(nvect))
#Interpolation
plt.figure(figsize=(8,10))
for j in range(0,len(nvect)):
#Current n:
    n = nvect[j] #n is the number of intervals.
    
    na = 1001 #Number of points to plot approximation
    xj = np.linspace(xl,xr,n+1) #equispaced points
    xx = np.linspace(xl,na) #points to plot approximation
    
    intval = 0
    for i in range(0,n+1):
        L_i = 1;
        for k in range(0,n+1):
            if k!=i:
                L_i = L_i*(xs-xj[k])/(xj[i]-xj[k]) #symbolic form
        
        Li_int = sympy.integrate(f(i)*L_i[i],xr))
        #Li = sympy.lambdify(xs,Li_int)
        intval = intval + Li_int
   
    err[j] = np.abs(int_exact-intval)
    
plt.scatter(nvect,err,color='r',s=150,label='Global,equispaced points')

我收到以下错误：

Li_int = sympy.integrate(f(i)*L_i[i],xr))

TypeError: 'Mul' object is not subscriptable

我不知道如何解决这个问题