# Forcing Exact Outputs for Integrate [closed]

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?

• I get an exact result - try restarting kernel and re-do... – ciao Apr 18 '15 at 21:49
• Tried it. Still getting results like the above. – PPMC Apr 18 '15 at 21:55
• What version of MMA and what O/S are you on? – ciao Apr 18 '15 at 21:57
• Running Mathematica version 9.0.1.0 on Mac OS X version 10.9.5. – PPMC Apr 18 '15 at 21:58
• Hypothesis non fingo... as you can see here, exact results (on 9.0.1 Windows) – ciao Apr 18 '15 at 22:07

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.

• Perfect. Thanks! – PPMC Apr 18 '15 at 23:57
• Give a positive vote then :) – Nick Mpountouropoulos Apr 19 '15 at 0:01
• Someday I'll have enough reputation to do that... :) – PPMC Apr 19 '15 at 0:11
• 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. – Michael E2 Apr 19 '15 at 0:46
• I'll check it out. I am new in this community!Thank's. – Nick Mpountouropoulos Apr 19 '15 at 0:53