I need help with this because it is not working

Question

Use integration by parts to evaluate the integral:

∫₁⁵ (ln(𝑟)) / (𝑟^4) 𝑑𝑟 = 

 

Report your answer accurate to at least 6 decimal places.

Answer 1

desmos.com/calculator/xek1tarlfm

Answer 2

What have you chosen to define as your u and dv? When given a natural log in an integration by parts problem I like to use the ln as my u because its respective du becomes much easier to work with. In this case, the du is simply (1/r)dr, which matches the form of the rest of the integral (the r^-4 term) nicely and should allow us to simplify.

That then leaves the r^-4 dr term to be our dv, so its resulting v would be -1/(3r^3).While the uv term is a little messy, the ∫vdu term is a very straightforward antiderivative: ∫-1/(3r^4) dr. Just remember the formula for integration by parts is uv - ∫vdu, so subtracting the negative will result in the second term being added.

From here the challenge will be correctly evaluating the result over the interval. Depending on what you're using for your computations, adequate and proper parentheses will be necessary.

Hope this helps!