| Integral of Exponential 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.exp(sp.exp(-x)) - x**(-sp.E)  # 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 = (5 - sp.exp(2*x))**2  # 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 'r'
r = sp.symbols('r')  # Define the symbolic variable 'r'

# 3rd: Define the integrand
integrand = 1 / (1 - sp.exp(-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
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 'f'
f = sp.symbols('f')  # Define the symbolic variable 'f'

# 3rd: Define the integrand
integrand = sp.sqrt(1 - sp.exp(f)) / sp.exp(-f)  # 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

 

 

 

 

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

# 3rd: Define the integrand
integrand = sp.exp(sp.tan(x)) / sp.cos(x)**2  # 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
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