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

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

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

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

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

# 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 / (7 * v**2 + 4)  # 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
print(integral_result)  # Print the result of the integral

# 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 = z * sp.sqrt(1 + 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
print(integral_result)  # Print the result of the integral

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

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

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

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

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

# 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 = sp.acos(2 * s)  # 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)  # Print the result of the integral