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Mathematica Mistake?

  1. Sep 17, 2009 #1
    There is something pretty strange going on with mathematica right now.

    When I do the following function
    Code (Text):
    Integrate[(n x + 1)^2,x]
    I get the result
    [tex]\frac{(1+nx)^3}{3n}[/tex]
    Expanded this is
    [tex]\frac{1}{3 n}+x+n x^2+\frac{n^2 x^3}{3}[/tex]

    However this is not the result I get if I integrate the individual parts of the expansion
    [tex](nx+1)^2=1+2nx+n^2x^2[/tex]
    and add the results of the integrals
    i.e.
    Code (Text):
    Integrate[n^2 x^2, x] + Integrate[2*n*x, x] + Integrate[1, x]
    which gives me
    [tex]x+n x^2+\frac{n^2 x^3}{3}[/tex]

    Please tell me I am missing somthing obvious and mathematica isn't making a mistake?
     
  2. jcsd
  3. Sep 17, 2009 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    If you integrate w.r.t x, then 1/(3n) is a constant. You have not given integration boundaries, so this is allowed. In other words, since D[1/(3n), x] = 0, both results differentiate back to [itex](nx + 1)^2[/itex].
     
  4. Sep 17, 2009 #3
    Granted it is allowed, why would it choose such an esoteric constant? Like you said I didn't provide it any boundary conditions, so whats so special about this constant? It seems rather unusal to me, and its not a behavior I have seen from the software before when performing integration that I am aware of.
     
  5. Sep 17, 2009 #4

    Dale

    Staff: Mentor

    The constant is not particularly esoteric. It is a direct result of applying the chain rule to (n x + 1)^2. In any case, as mentioned above integration is only defined up to a constant, so there is no mistake here other than the fact that the constant is not explicitly mentioned (which I think it should do).
     
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