0
$\begingroup$

I have a big function of 6 variables in total - x1, x11, x2, x22, x3, x33.

f6[x1_, x2_, x3_, x11_, x22_, x33_] := -((
3 (4 (x1 - x11)^2 - (x2 - x22)^2 - (x3 - x33)^2) ((x2 - 
x22)^2 + (x3 - x33)^2))/(
8 \[Pi] ((x1 - x11)^2 + (x2 - x22)^2 + (x3 - x33)^2)^(7/2)));

I need to use indefinite integral because i need to get a symbolic expression.

I am using Wolfram Mathematica 7.

I tried something very simple:

FullSimplify@
Integrate[f6[x1, x2, x3, x11, x22, x33], x1, x2, x3, x11, x22, x33]

I waited for about 30 minutes and nothing happened. It is obviously a complicated integral.

Can anyone tell me how to solve this problem? Is there a way to simplify the function so the integration is easier for Mathematica?

Improve this question
$\endgroup$
6
  • $\begingroup$ Try FullSimplify@ Integrate[f6[x1, x2, x3, x11, x22, x33], {x1, x2, x3, x11, x22, x33}] $\endgroup$
    – Ulrich Neumann
    Commented Aug 26, 2020 at 10:24
  • $\begingroup$ Thank you for your answer, Ulrich! Mathematica managed to integrate it. However, I get a giant function with a lot of Assumptions and If statements. Also, it appears that integrated expression has both Real and Imaginary part, which is a bad news for me. $\endgroup$
    – user57225
    Commented Aug 26, 2020 at 11:00
  • $\begingroup$ Without knowledge of your function it's difficult to give helpful answers! $\endgroup$
    – Ulrich Neumann
    Commented Aug 26, 2020 at 11:08
  • $\begingroup$ @UlrichNeumann I have not been able to find documentation for your suggested syntax. Has this been changed in newer versions? $\endgroup$
    – Natas
    Commented Aug 26, 2020 at 14:41
  • $\begingroup$ @Natas Sorry, please forget my comment. In this form integraion is done with integration variable x1 in the range x2...x33 and singularities x2,x3,x11,x22 $\endgroup$
    – Ulrich Neumann
    Commented Aug 27, 2020 at 6:50

1 Answer 1

Reset to default
2
$\begingroup$

If you change the order of integration

Integrate[f6[x1, x2, x3, x11, x22, x33], x1 , x11, x2, x22, x3, x33]

the integral is evaluated in 120seconds.

Improve this answer
$\endgroup$
5
  • $\begingroup$ Nothing is happening in my case. Which version of Mathematica are you using? $\endgroup$
    – user57225
    Commented Aug 27, 2020 at 7:53
  • $\begingroup$ My version is v12 (Windows 10) $\endgroup$
    – Ulrich Neumann
    Commented Aug 27, 2020 at 8:04
  • $\begingroup$ OK Ulrich. I appreciate your answers and effort! $\endgroup$
    – user57225
    Commented Aug 27, 2020 at 8:14
  • $\begingroup$ Hey Ulrich. One more question. Does the expression you get have any imaginary parts? $\endgroup$
    – user57225
    Commented Aug 27, 2020 at 8:30
  • 1
    $\begingroup$ @user57225 Yes it's imaginary! Sorry the expression is quite huge, that's why I couldn'd display it $\endgroup$
    – Ulrich Neumann
    Commented Aug 27, 2020 at 8:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.