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Char. Limit
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Homework Statement
So I thought of an interesting problem, and here it is:
Solve [tex]\int \frac{1}{f'(x)} df(x) = g(x)[/tex] for f(x).
Now, I checked Wolfram-Alpha to see if an answer existed, and they gave me this:
[tex]f(x) = c_1 e^{\int \frac{1}{g(\xi)} d\xi}[/tex]
But, you know that Wolfram-Alpha doesn't show steps. So I want to know how they got from start to finish. I checked the solution, and it seems to work, but how did they get there?
Note that I have taken all three Calculus classes, but no differential equations experience.
EDIT: As a further question, how do you integrate with respect to a function? Is that even defined?
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