| Repeated Linear Factors - Code |

Dec. 21, 2024, 4:30 p.m.

 

 

 

 

1. What is the python code for this problem:

 

# 1st: Import the sympy module
import sympy as sp  # Import sympy for symbolic computation

# 2nd: Define the variable 'g'
g = sp.symbols('g')  # Define the symbolic variable 'g'

# 3rd: Define the integrand
integrand = 1 / (2 + g)**3  # Define the function to integrate

# 4th: Perform the integration with respect to 'g'
integral_result = sp.integrate(integrand, g)  # Compute the integral

# 5th: Display the result
print(integral_result)  # Print the result of the integral

 

 

 

 

2. What is the python code for this problem:

 

# 1st: Import the sympy module
import sympy as sp  # Import sympy for symbolic computation

# 2nd: Define the variable 'x'
x = sp.symbols('x')  # Define the symbolic variable 'x'

# 3rd: Define the integrand
integrand = (5 * x - 3) / (x**4 + x**3 - 2 * x**2)  # Define the function to integrate

# 4th: Perform partial fraction decomposition
partial_fractions = sp.apart(integrand, x)  # Perform partial fraction decomposition

# 5th: Integrate the result
integral_result = sp.integrate(partial_fractions, x)  # Compute the integral

# 6th: Display the result
print(integral_result)  # Print the result of the integral

 

 

 

 

3. What is the python code for this problem:

 

# 1st: Import the sympy module
import sympy as sp  # Import sympy for symbolic computation

# 2nd: Define the variable 'y'
y = sp.symbols('y')  # Define the symbolic variable 'y'

# 3rd: Define the integrand
integrand = (6 * y - 11) / (y - 1)**2  # Define the function to integrate

# 4th: Perform the integration
integral_result = sp.integrate(integrand, y)  # Compute the integral

# 5th: Display the result
print(integral_result)  # Print the result of the integral

 

 

 

 

4. What is the python code for this problem:

# 1st: Import the sympy module
import sympy as sp  # Import sympy for symbolic computation

# 2nd: Define the variable 'm'
m = sp.symbols('m')  # Define the symbolic variable 'm'

# 3rd: Define the integrand
integrand = 2 * m / ((m - 2)**2 * (m + 2))  # Define the function to integrate

# 4th: Perform the integration
integral_result = sp.integrate(integrand, m)  # Compute the integral

# 5th: Display the result
print(integral_result)  # Print the result of the integral

 

 

 

 

5. What is the python code for this problem:

 

# 1st: Import the sympy module
import sympy as sp  # Import sympy for symbolic computation

# 2nd: Define the variable 'x'
x = sp.symbols('x')  # Define the symbolic variable 'x'

# 3rd: Define the integrand
integrand = (3*x + 5) / ((x - 1)**2 * (x + 1))  # Define the function to integrate

# 4th: Perform the integration
integral_result = sp.integrate(integrand, x)  # Compute the integral

# 5th: Display the result
print(integral_result)  # Print the result of the integral
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