sympy.integrals.rationaltools.ratint() in python

With the help of ratint() method, we can compute the indefinite integration of a rational function. If a function is a rational function, their is a Lazard Rioboo Trager and the Horowitz Ostrogradsky algorithms that are implemented in this method.

Syntax : ratint(f, x, **flags)

Return : Return the integrated function.

Example #1 :

In this example we can see that by using ratint() method, we are able to compute the indefinite integration of a rational function and return the integrated function by using this method.

# import ratint
from sympy.integrals.rationaltools import ratint
from sympy.abc import x

# Using ratint() method
gfg = ratint((x**5 - 2*x**3 + x - 2)/12, x)

print(gfg)

Output :

x**6/72 - x**4/24 + x**2/24 - x/6

Example #2 :

# import ratint
from sympy.integrals.rationaltools import ratint
from sympy.abc import y

# Using ratint() method
gfg = ratint((3*y**3 + 4*x**2 + y - 2), y)

print(gfg)

Output :

3*y**4/4 + y**2/2 + y*(4*x**2 - 2)