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Help with integration (1) involving integration by parts etc

  1. Feb 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Solve for indefinite integral of
    (7x^3)/sqr(4+x^2)(dx)

    2. Relevant equations
    I just can't seem to find the right solution.


    3. The attempt at a solution
    First of all, we can just factor the 7 out of the integral for now since it is only a constant.
    the inverse square root of (4+x^2) looks like arctan(x/2).
    So I set 1/(4+x^2) up as dv, and so V would equal arctan(x/2). U is then x^3, and du is 3x^2.
    However, the integrals just don't seem to simplify. Please help.
     
  2. jcsd
  3. Feb 25, 2009 #2

    lanedance

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    how about looking at trig substitution - in particular what trig identity could simplfy the denominator
     
  4. Feb 25, 2009 #3

    Dick

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    Substitution again. Try u=x^2+4. You have a left over x^2 in the numerator. But x^2=u-4. Try the easy stuff before you resort to the hard stuff.
     
  5. Feb 25, 2009 #4
    I did it, and ended up with the integral of (u^2-4u) over square root of u, all multiplied by the constant 7/2. After a lengthy algebra session, I ended up with a huge answer, that wasn't correct... What did I do wrong?
     
  6. Feb 25, 2009 #5

    Dick

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    I ended up with basically (u-4)*du/sqrt(u) forgetting the constants. What did you do? I think you have an extra u in the numerator which doesn't belong there.
     
  7. Feb 25, 2009 #6
    Ah, there we go. I forgot to take out an x for du. Thanks.
     
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