Integral(e^(ab))da= e^(ab)*b^-1 Why?

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Integral(e^(ab))da= e^(ab)*b^-1 Why?

Mathematics
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As, going the other way: if I differentiate the right equation with respect to a, b doesn't dissapear, as it is a constant, then why does a b^-1 materialise in the antiderivative?
i take it thats a partial and not b(a)?
\[D_a(exp({ab}))=exp(ab)*(ab)'\] \[D_a(exp({ab}))=exp(ab)(a'b+ab')\] or maybe if bs a constant \[D_a(exp({ab}))=exp(ab)*b\]

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Other answers:

we need the 1/b to catch it; 1/b * b = 1
in other words, if we dont put something there to catch the "b" that flies out we dont get the derivative we are looking for
Dx is a way to notate a derivative operation on something.
Da means take the derivative of this stuff with respect to a
go ahead and replace b with your favorite constant thats not 0
youll see that if we dont have a 1/2 in the antiderivative that we end up with : exp(2a)*2 which is NOT what we are trying to undo.
so we apply a useful form of 1 into the antiderivative to help us out; since 1* anything doesnt change its value; we need a "2", or a "b" as the case may be, so lets use 2/2 and just pull out the 1/2 for later
Thanks, after writing that out it clicked.
:) youre welcome

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