| Integral of Inverse Hyperbolic Functions - Code |

Dec. 21, 2024, 3:01 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 'h'
h = sp.symbols('h')  # Define the symbolic variable 'h'

# 3rd: Define the integrand
integrand = sp.ln(h) / sp.sqrt(sp.ln(h)**2 - 4)  # Define the function to integrate

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

# 5th: Display the result
sp.pprint(integral_result)  # Pretty print the result

 

 

 

 

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 'f'
f = sp.symbols('f')  # Define the symbolic variable 'f'

# 3rd: Define the integrand
integrand = f / (f**4 - 16)  # Define the function to integrate

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

# 5th: Display the result
sp.pprint(integral_result)  # Pretty print the result

 

 

 

 

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 's'
s = sp.symbols('s')  # Define the symbolic variable 's'

# 3rd: Define the integrand
integrand = 1 / sp.sqrt(sp.exp(-4*s) - 4)  # Define the function to integrate

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

# 5th: Display the result
sp.pprint(integral_result)  # Pretty print the result

 

 

 

 

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 'z'
z = sp.symbols('z')  # Define the symbolic variable 'z'

# 3rd: Define the integrand
integrand = sp.cos(z) / sp.sqrt(sp.sin(z)**2 - 81)  # Define the function to integrate

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

# 5th: Display the result
sp.pprint(integral_result)  # Pretty print the result

 

 

 

 

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 'z'
z = sp.symbols('z')  # Define the symbolic variable 'z'

# 3rd: Define the integrand
integrand = 1 / (z * sp.sqrt(9 - z**4))  # Define the function to integrate

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

# 5th: Display the result
sp.pprint(integral_result)  # Pretty print the result