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

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The integral of 1/(1-x) is -ln(1-x). This conclusion is reached by differentiating both ln(1-x) and -ln(1-x) to determine which yields the original function. The negative sign arises because the derivative of the inner function (1-x) is -1, necessitating division by -1 during integration. Thus, the correct integral reflects this adjustment. Understanding this relationship is crucial for accurate integration in calculus.
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is the integral of 1/(1-x)
ln(1-x) or -ln(1-x)??
 
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onie mti said:
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)
 
onie mti said:
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.
 
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