from sympy import symbols, integrate

Define the variables

x = symbols('x')

Define the integral

integral_expression = 7 * x / (x + 1)**2

Evaluate the definite integral

result = integrate(integral_expression, (x, 1, 5)) result-7log(2) - 7/3 + 7log(6)-7log(2) - 7/3 + 7log(6)successThe value of the definite integral

$\int_{1}^{5} \frac{7x}{(x+1)^2} \, dx$

is:

$7\ln(6) - 7\ln(2) - \frac{7}{3}$

If you'd like, I can simplify this further or explain the steps. Let me know!

Here are some follow-up questions:

1. Would you like to see a step-by-step explanation of how this integral was solved?
2. Are you interested in the general technique for solving integrals of this form?
3. Do you want to verify the solution numerically?
4. Should I explain the logarithmic terms in more depth?
5. Do you want to learn about substitutions or transformations used in solving integrals?

Tip: When dealing with rational functions, consider substitutions or partial fraction decomposition to simplify the integral.