Python | sympy.Integral() method

With the help of sympy.Integral() method, we can create an unevaluated integral of a SymPy expression. It has the same syntax as integrate() method. To evaluate an unevaluated integral, use the doit() method.

Syntax: Integral(expression, reference variable)

Parameters:
expression – A SymPy expression whose unevaluated integral is found.
reference variable – Variable with respect to which integral is found.

Returns: Returns an unevaluated integral of the given expression.

Example #1:

# import sympy
from sympy import *

x, y = symbols('x y')
expr = x**2 + 2 * y + y**3
print("Expression : {} ".format(expr))

# Use sympy.Integral() method
expr_intg = Integral(expr, x)

print("Integral of expression with respect to x : {}".format(expr_intg))
print("Value of the Integral : {} ".format(expr_intg.doit()))

Output:

Expression : x**2 + y**3 + 2*y 
Integral of expression with respect to x : Integral(x**2 + y**3 + 2*y, x)
Value of the Integral : x**3/3 + x*(y**3 + 2*y) 

Example #2:

# import sympy
from sympy import *

x, y = symbols('x y')
expr = y**3 * x**2 + 2 * y*x + x * y**3
print("Expression : {} ".format(expr))

# Use sympy.Integral() method
expr_intg = Integral(expr, x, y)

print("Integral of expression with respect to x : {}".format(expr_intg))
print("Value of the Integral : {} ".format(expr_intg.doit()))

Output:

Expression : x**2*y**3 + x*y**3 + 2*x*y 
Integral of expression with respect to x : Integral(x**2*y**3 + x*y**3 + 2*x*y, x, y)
Value of the Integral : x**2*y**2/2 + y**4*(x**3/12 + x**2/8)