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

# 2nd: Define the variable 'm'
m = sp.symbols('m')  # Define 'm' as a symbolic variable

# 3rd: Define the function to integrate
f = 1 / (m * sp.sqrt(m - 1))  # Define the function f(m)

# 4th: Compute the definite integral of the function from 2 to 4
definite_integral = sp.integrate(f, (m, 2, 4))  # Perform the definite integration

# 5th: Display the result
sp.pprint(definite_integral)  # 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 'v' as a symbolic variable

# 3rd: Define the function to integrate
f = (v + 1) / (v**2 + 1)  # Define the function f(v)

# 4th: Compute the definite integral of the function from 4 to 6
definite_integral = sp.integrate(f, (v, 4, 6))  # Perform the definite integration

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

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

# 2nd: Define the variable 'g'
g = sp.symbols('g')  # Define 'g' as a symbolic variable

# 3rd: Define the function to integrate
f = sp.sqrt(3 * g) - 2  # Define the function f(g)

# 4th: Compute the definite integral of the function from -1 to 1
definite_integral = sp.integrate(f, (g, -1, 1))  # Perform the definite integration

# 5th: Display the result
sp.pprint(definite_integral)  # 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 'm' as a symbolic variable

# 3rd: Define the function to integrate
f = m * sp.sqrt(8 - m**2)  # Define the function f(m)

# 4th: Compute the definite integral of the function from -1 to 2
definite_integral = sp.integrate(f, (m, -1, 2))  # Perform the definite integration

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

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

# 2nd: Define the variable 'x'
x = sp.symbols('x')  # Define 'x' as a symbolic variable

# 3rd: Define the function to integrate
f = 5 * x**4 + 5  # Define the function f(x)

# 4th: Compute the definite integral of the function from 1 to 2
definite_integral = sp.integrate(f, (x, 1, 2))  # Perform the definite integration

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