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Double exponential integration (a,∞) - how to implement.

  1. Mar 28, 2014 #1
    NOTE: This isn't homework.

    So I'm trying to integrate a really awkward integral with limits from a to infinity;

    [itex]\int^{∞}_{30471.2729807}(\frac{83.1451 * 373.15}{X})-(\frac{83.1451 * 373.15}{X-30.4811353}-\frac{5534906.5380409}{X^2})dX[/itex]

    Since the Simpson's and Trapezoidal would be really awkward to use with these (I literally used a limit of 30471.2729807 to 1000000000 (lol)) I tried to search for other alternatives, and I found this.

    I can't understand how this is implemented though. This transformation

    [itex]\int^{∞}_{a}f(X)dX → \int^{∞}_{0}f(X+a)dX[/itex]

    is bothering me as well. Can someone point me where a step-by-step algorithm of the method's implementation is made; or if possible, someone tell me how it was done?
  2. jcsd
  3. Mar 28, 2014 #2


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    It's a transformation of variables: let u=X+a; then for X=(a,inf) we get u=(0,inf), and dX = du.

    All they did was skip the formal analysis and went directly to the result: f(u) = f(X+a).
  4. Mar 28, 2014 #3
    I see. Got it.
  5. Mar 28, 2014 #4


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