Integration by Parts does it matter which is f(x) and g(x)

Integral of e^x*cos(x) dx . This is done by integration by parts twice .
But does it matter which is f(x) or g(x)
The formula , integral of f(x)g'(x) dx = f(x)g(x) - integral of f'(x)g(x) dx .
e^x will integrate or differentiate infinite times and never be zero .
Similarly cos(x) will differentiate or integrate infinite times and still be left with sin or cos.
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