MHB Finding the Integral of 1/(1-x): ln(1-x) or -ln(1-x)?

[onie mti]

is the integral of 1/(1-x)
ln(1-x) or -ln(1-x)??

 

[Opalg]

is the integral of 1/(1-x)
ln(1-x) or -ln(1-x)??

You can find out by differentiating $\ln(1-x)$ and $-\ln(1-x)$, and seeing which one gives the correct answer. (Wink)

 

[Pindrought]

is the integral of 1/(1-x)
ln(1-x) or -ln(1-x)??

The integral of 1/(1-x) is -(ln(1-x)) which = -ln(1-x)

It is negative, because the derivative of the inside (1-x) is -1, so you have to divide by the -1 when finding the integral, which would in this case just make it negative.