1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Help with an integral

  1. Mar 11, 2014 #1
    1. The problem statement, all variables and given/known data

    ∫(x^3)/(x^2 + 9) dx

    2. Relevant equations

    3. The attempt at a solution

    This question can be solved using long division, but I just wanted to know why I can't do it this other way.

    So I start with one substitution, t = x^2, dt = 2xdx.
    By taking out 1/2 from the integrand, I can make the integral:
    ∫(t dt)/(t + 9)
    Then, using another substitution, u = t + 9, t = u - 9, du = dt
    I make the equation into:
    ∫(u - 9)du / (u)

    Separating the integrand into two separate integrals, I can solve it, and it becomes:
    1/2 [(x^2 + 9) - 9ln(x^2 + 9)] + C
    However, this isn't the right answer because the right answer does't contain a 9/2 constant inside. Why can't I solve this integral this way? Thanks for any help in advance.
  2. jcsd
  3. Mar 11, 2014 #2


    Staff: Mentor

    Your answer is correct, and differs from the result obtained by long division by a constant. After all, C and C + 9/2 are just constants. If you differentiate both answers, you get the integrand you started with.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted