#!/usr/bin/env python
# coding: utf-8

# In[1]:


from sympy import *
init_printing(use_unicode=True, wrap_line=False, no_global=True)
import matplotlib.pyplot as plt
get_ipython().run_line_magic('matplotlib', 'notebook')
from sympy.abc import x,y


# In[2]:


denominator = x**4 + 2*x**2 + 1
factor(denominator)


# In[3]:


plot_implicit(Eq(denominator, y), (x, -0.6, 0.6), (y, 0, 2))


# In[4]:


plot_implicit(Eq(denominator, y), (x, -6, 6), (y, 0, 1400))


# In[5]:


denominator = 1 / (x**4 + 2*x**2 + 1)
factor(denominator)


# In[6]:


plot_implicit(Eq(denominator, y), (x, -6, 6), (y, 0, 1))


# In[7]:


numerator = x**3 * sin(x)**2
numerator


# In[8]:


plot_implicit(Eq(numerator, y), (x, -6, 6), (y, -120, 120))


# In[9]:


wifieqn = numerator*denominator
factor(wifieqn)


# In[10]:


plot_implicit(Eq(wifieqn, y), (x, -6, 6), (y, -0.4, 0.4))


# In[11]:


integ = integrate(wifieqn, (x, -5, 5))
integ


# In[12]:


integ.doit()