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The indefinite integral of a given function is only defined up to an additive constant
(and your results differ by a constant)
The definte integral, for example
sage: ii=integrate(100exp(-1/2x^2/8^2)*cos(x),x,0,+oo);
sage: ii
400sqrt(pi)sqrt(2)*e^(-32)
is the same in Mathematica (WolframAlpha)
