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Difficult Integral

  1. Oct 10, 2016 #1
    1. The problem statement, all variables and given/known data
    Hi, I'm doing a variation of parameters problem for my differential equations class. It requires solving the integral:

    ∫ex t-2 dt

    I am sure my professor did not give me an impossible integral and that there is some algebraic "trick" to solving it, but despite going through several iterations of integration by parts I am unable to find it (I have encountered similar problems before but my memory of them is fuzzy).

    2. Relevant equations

    3. The attempt at a solution
    Several Integration by parts attempts. I looked for a cancellation.
  2. jcsd
  3. Oct 10, 2016 #2


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    Both ##x## and ##t## in there?

    Please give us a statement of the original problem and your work so far. How do we know your integral is correct?
  4. Oct 10, 2016 #3


    Staff: Mentor

    If you have written the integral correctly, it's a very simple one to evaluate. Here ex can be treated as a constant.
  5. Oct 10, 2016 #4
    Oh I'm so sorry! I mis-wrote the integral. It is:

    ∫e-x2 x-2 dt
  6. Oct 10, 2016 #5

    Ray Vickson

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    If you mean ##\int e^{-x^2} x^{-2} \, dt##, that is easy: it is ##e^{-x^2} x^{-2} \int dt = e^{-x^2}x^{-2} (t+C)##. If you mean ##\int e^{-x^2}x^{-2} \, dx##, that is a different matter entirely. The integral is do-able in terms of the so-called error function.

    On the other hand, if in the first form above the ##x## is a function of ##t##, the integral may be intractable for certain functions ##x = x(t)##.
    Last edited: Oct 10, 2016
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