# Integrating to produce a log function

• May 6th 2011, 07:04 PM
aonin
Integrating to produce a log function
Hey everyone, just wondering whats the difference when I integrate:
$\int\dfrac{1}{-x+1}\,dx$
it be integrated in 2 ways
$-\int\dfrac{1}{x-1}=-ln(x-1)$

OR

$-\int\dfrac{-1}{-x+1}\,dx=-ln(-x+1)$

are those 2 solutions different? or is there some log manipulation to make
$-ln(x-1)\text{be the same as} -ln(-x+1)$
• May 6th 2011, 07:33 PM
Deveno
as you can see, -ln(x-1), and -ln(-x+1) have different domains.

the first function is only defined for x > 1, and the second is only defined for x < 1.

to circumvent these difficulties, one often sees the antiderivative as -ln|x-1|, which is defined for all x ≠ 1.
• May 7th 2011, 02:29 AM
aonin
ah ok i get what you mean now. Thanks for the help :D