MATLAB: Wrong integration result with R2011b

cosintintegrationMATLABr2011bSymbolic Math Toolboxsyms

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?

Best Answer

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.
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