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I am trying to solve the indefinite integral with user-defined rules. the integral expression and details are shown below

my integral

where the P is a function of a,b and c. and I would like Mathematica to follow what I did. I keep struggling for a very long time, but I could only make the very beginning part work, the code I had right now is 

TT = \[Integral]\[Integral]\[Integral]D[P[x1, x2, x3, t]*x1, x1]*x1^r*
     x2^s*x3^n \[DifferentialD]x1 \[DifferentialD]x2 \
\[DifferentialD]x3

ExpandAll[TT]

I tried using the ExpandAll to expand out the expression into 2 different parts, but it does not work.

any help from anyone will be very grateful.

Sincerely, Li

J. M.'s missing motivation
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  • check this https://mathematica.stackexchange.com/q/148/49157 – Mr Puh May 04 '20 at 06:26
  • Hi Puh, I think it is different from what I want, I think my question is focused on developing specific rules to let MATHEMATICA follow, besides MATHEMATICA does try to solve the indefinite integral, but without giving more rules and instructions, it is not able to end up with the solution I expect. as for the information you shared, it is about the steps and details which MATHEMATICA used to solve symbolic math functions. anyway, thanks for your help. – xiaofu li May 04 '20 at 21:18
  • I am not sure whether giving some rules to MATHEMATICA will work or not, for example, rule1 = \!\(\*SuperscriptBox[\(P\), TagBox[ RowBox[{"(", RowBox[{"1", ",", "0", ",", "0", ",", "0"}], ")"}], Derivative], MultilineFunction->None]\)[x1, x2, x3, t]*\[DifferentialD]x1 -> \[DifferentialD]p;, any help from anyone is very grateful – xiaofu li May 04 '20 at 22:09
  • @xiaofuli Have you given Rubi - the Rule-Based Integrator a try in your case? – MarcoB May 05 '20 at 03:46
  • Hi MarcoB, I did not go through it carefully, but I will definitely give it a try, hopefull I could make something work. – xiaofu li May 07 '20 at 04:18

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