Wrong integration result with R2011b

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I get a wrong result with R2011b when doing the folloing integration:
>> syms x
>> syms a
>> int(x/2+sin(2*a*x)/(4*a),x)
ans =
x^2/4 - cos(a*x)^2/(4*a^2)
>> int(x/2,x) + int(sin(2*a*x)/(4*a),x)
ans =
x^2/4 - cos(2*a*x)/(8*a^2)
So the second result is the correct one, the first is wrong (when transforming the second result to the form of the first one there is a -1/(8*a^2) missing). When using R2010b I get the correct result when calculating int(x/2+sin(2*a*x)/(4*a),x). Is this a bug in R2011b?
  1 Comment
Jan
Jan on 27 Mar 2012
Does this mean, that you are missing a constant expression after calculatingthe integral?

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Accepted Answer

Alexander
Alexander on 27 Mar 2012
Both answers are correct. Let me quote Wikipedia's entry for Constant of integration:
In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) is only defined up to an additive constant, the constant of integration.
Since -1/(8*a^2) does not depend on x it is just another constant of integration. You can also verify this if you derive both results with respect to x.

More Answers (1)

Daniel
Daniel on 27 Mar 2012
Yes, you are right, I didn't take that into account, thanks!
Still, I find it strange, that there are different results for different version, but now that I recognized that everything is fine, I can live with it.

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