| Integral of Hyperbolic Functions - Code |

Dec. 21, 2024, 3 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 = sp.sinh(x) / (1 + sp.cosh(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
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 'x'
x = sp.symbols('x')  # Define the symbolic variable 'x'

# 3rd: Define the integrand
integrand = sp.cosh(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
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 'v'
v = sp.symbols('v')  # Define the symbolic variable 'v'

# 3rd: Define the integrand
integrand = 1 + 2 * sp.sinh(4*v)**2  # Define the function to integrate

# 4th: Perform the integration with respect to 'v'
integral_result = sp.integrate(integrand, v)  # 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 'm'
m = sp.symbols('m')  # Define the symbolic variable 'm'

# 3rd: Define the integrand
integrand = m * sp.cosh(m**2 + 3)  # 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
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 'n'
n = sp.symbols('n')  # Define the symbolic variable 'n'

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

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

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