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Integration

\int \frac{1}{kx}\ dx

where k is a constant.

Does this equal

\frac{1}{k}\ln x

\frac{1}{k}\ln kx

Differentiating gives me the same original expression, but substituting values of x does not.

Any help, thanks...

(edited 10 years ago)

Reply 1

tory88

(1/k)*ln(x) - you can take a factor of (1/k) out before doing the integration.

Reply 2

fayled

Actually, to answer my own question, It equals both, because you can use the laws of logs to expand the latter, and one part is just a constant.

So I would recieve credit in an exam (although the first is more simple) for either way, right?

Reply 3

Felix Felicis

Original post by fayled

Indeed, don't quote me here, but I think both differentiate to the same thing by the uniqueness theorem of anti-derivatives (or whatever it's called) i.e. both integrals differ by a constant of integration.

If you slap on limits, it should evaluate to the same thing