| Algebraic Substitution - Code |

Dec. 21, 2024, 3:53 p.m.

 

 

 

 

1. What is the python code for this problem:

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

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

# 3rd: Define the integrand
integrand = (1 + sp.ln(x)) / x**3  # Define the function to integrate

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

# 2nd: Define the variable 't'
t = sp.symbols('t')  # Define the symbolic variable 't'

# 3rd: Define the integrand
integrand = sp.sin(sp.sqrt(t))  # Define the function to integrate

# 4th: Perform the integration with respect to 't'
integral_result = sp.integrate(integrand, t)  # Compute the integral

# 5th: 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 mathematics

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

# 3rd: Define the integrand
integrand = sp.exp(2 * x) * sp.sqrt(1 + sp.exp(x))  # Define the function to integrate

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

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

# 3rd: Define the integrand
integrand = 1 / (1 + sp.cos(r))  # Define the function to integrate

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

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

# 3rd: Define the integrand
integrand = sp.exp(2 * m) / (sp.exp(m) + 1)  # Define the function to integrate

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

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