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I'm trying to compute the following triple integral:

Integrate[
 Integrate[
  Integrate[
   E^(-v1 - v2 - v3) (v1 + v2 + v3)/3, {v3, 2 v1 - 5/2 v2, v2}], {v2, 
   4 v1/7, 5 v1/7}], {v1, 0, Infinity}]

I'm hoping to get the exact answer (as messy as it might be), but when I evaluate this (or even just the inner two of three integrals), Mathematica computes decimal approximations, rather than the fractions and powers of e that I need. For example, the inner two integrals evaluate to:

E^(-6.5 v1) (E^(4.35714 v1) (-0.777778 - 0.833333 v1) + 
   E^(4.07143 v1) (0.333333 + 0.404762 v1) + 
   E^(4.57143 v1) (0.444444 + 0.428571 v1))

but I'm fairly certain each of those coefficients is actually the decimal approximation of a rational number. Is there a way to force Mathematica to show me the exact expression instead?

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  • 1
    $\begingroup$ I get an exact result - try restarting kernel and re-do... $\endgroup$ – ciao Apr 18 '15 at 21:49
  • $\begingroup$ Tried it. Still getting results like the above. $\endgroup$ – PPMC Apr 18 '15 at 21:55
  • $\begingroup$ What version of MMA and what O/S are you on? $\endgroup$ – ciao Apr 18 '15 at 21:57
  • $\begingroup$ Running Mathematica version 9.0.1.0 on Mac OS X version 10.9.5. $\endgroup$ – PPMC Apr 18 '15 at 21:58
  • 1
    $\begingroup$ Hypothesis non fingo... as you can see here, exact results (on 9.0.1 Windows) $\endgroup$ – ciao Apr 18 '15 at 22:07
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Trace[Integrate[
  Integrate[
   Integrate[
    E^(-v1 - v2 - v3) (v1 + v2 + v3)/3, {v3, 2 v1 - 5/2 v2, v2}], {v2,
     4 v1/7, 5 v1/7}], {v1, 0, Infinity}]]

Check one line before the result. I think this is what you want.

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  • $\begingroup$ Perfect. Thanks! $\endgroup$ – PPMC Apr 18 '15 at 23:57
  • $\begingroup$ Give a positive vote then :) $\endgroup$ – Nick Mpountouropoulos Apr 19 '15 at 0:01
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    $\begingroup$ Someday I'll have enough reputation to do that... :) $\endgroup$ – PPMC Apr 19 '15 at 0:11
  • $\begingroup$ You can format inline code and code blocks by selecting it and clicking the {} button above the edit window. The edit window help button ? is also useful for learning how to format your questions and answers. $\endgroup$ – Michael E2 Apr 19 '15 at 0:46
  • $\begingroup$ I'll check it out. I am new in this community!Thank's. $\endgroup$ – Nick Mpountouropoulos Apr 19 '15 at 0:53

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