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Square root integration problem

  1. Sep 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Integrate : f(t) = t3/ sqrt(t2+1)
    2. Relevant equations

    3. The attempt at a solution
    t2* t / sqrt(t2+1)

    let u = sqrt(t2+1)
    u2 = t2 +1
    t2 = u2 -1 -Eq 1

    du = t/sqrt(t2-1) dt
    dt = sqrt(t2-1)/t du -Eq 2

    Hence Substituting 1 and 2
    Integrate : f(t)
    = Integrate (u^2 -1) du

    Is this way correct? If not can give me the right way
  2. jcsd
  3. Sep 2, 2010 #2


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    Science Advisor

    Re: a

    Looks good to me. I think I would have been inclined to use the simpler [itex]u= t^2+ 1[/itex], du= 2t dt so that t dt= (1/2)du and [itex]t^2= u- 1[/itex].

    That would give
    [tex]\int t^2\sqrt{t^2+ 1}dt= \int(u- 1)(\sqrt{u}(1/2)du= (1/2)\int u^{3/2}- u^{1/2}du[/tex]
    but that will give the same thing as your integral.
    Last edited by a moderator: Sep 2, 2010
  4. Sep 2, 2010 #3
    Re: a

    Alrite Thanks!!
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