# coding: utf-8

# In[1]:

from sympy import *
E**(I*pi)+1


# In[4]:

x = Symbol('x')
expand( E**(I*x) )


# In[6]:

x = Symbol("x", real=True)
expand(exp(I*x), complex=True)


# In[7]:

tmp = series(exp(I*x), x, 0, 10)
pprint(tmp)


# In[8]:

pprint(re(tmp))


# In[9]:

pprint( series( cos(x), x, 0, 10) )


# In[10]:

pprint(series(sin(x), x, 0, 10))


# In[11]:

integrate(x*sin(x), x)


# In[12]:

integrate(x*sin(x), (x, 0, 2*pi))


# In[13]:

x, y, r = symbols('x,y,r')
2 * integrate(sqrt(r*r-x**2), (x, -r, r))
   


# In[18]:

r = symbols('r', positive=True)
circle_area = 2 * integrate(sqrt(r**2-x**2), (x, -r, r))
circle_area


# In[17]:

r = symbols('r', positive=True)
circle_area = circle_area.subs(r, sqrt(r**2-x**2))
circle_area


# In[21]:

r = symbols('r', positive=True)
circle_area = circle_area.subs(r, sqrt(r**2-x**2))
integrate(circle_area, (x, -r, r))


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