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

# 2nd: Define the variables 'z' and 'a'
z, a = sp.symbols('z a')  # Define symbolic variables 'z' and 'a'

# 3rd: Define the integrand
integrand = 1 / (1 + sp.sec(a) * z)  # 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

# 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 = sp.cos(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

# 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 = 1 / sp.sqrt(1 - sp.cos(9*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

# 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 = (1 - sp.cos(m)) / (1 + sp.cos(m))  # 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

# 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 = sp.tan(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