| Repeated Quadratic 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 = sp.symbols('g')  # Define the symbolic variable 'g'

# 3rd: Define the integrand
integrand = 1 / (g**4 + 4)  # Define the function to integrate

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

# 5th: Output the result
print("The integral is:", integral)  # 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
f = sp.symbols('f')  # Define the symbolic variable 'f'

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

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

# 5th: Output the result
print("The integral is:", integral)  # 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 = sp.symbols('y')  # Define the symbolic variable 'y'

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

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

# 5th: Output the result
print("The integral is:", integral)  # 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
p = sp.symbols('p')  # Define the symbolic variable 'p'

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

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

# 5th: Output the result
print("The integral is:", integral)  # 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
z = sp.symbols('z')  # Define the symbolic variable 'z'

# 3rd: Define the integrand
integrand = 1 / (z**2 + 4*z + 5)**2  # Define the function to integrate

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

# 5th: Output the result
print("The integral is:", integral)  # Print the result of the integral