All possible antiderivatives for Integration by Parts
Just had a quick inquiry with regards to the formula for Integration by Parts. If I'm not mistaken, the formula states that
However, in the case that I try to substitute an antiderivative with a valid constant, the formula does not appear to work. I attempted to use a simple product such as , using 7x as f′(x) and as g(x) respectively. I found that using for the antidervative for 7x does not work in the formula, while without the constant does indeed work. I am sure that I am missing something, however, why do both of these solutions not work, even though both are valid antiderivatives?