# Math Help - Integrating to produce a log function

1. ## 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
$-ln(x-1)\text{be the same as} -ln(-x+1)$

2. 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.

3. ah ok i get what you mean now. Thanks for the help