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How do you integrate of $\frac{1}{1 - x}$ $1/(1-x)$ ?

1 Answer

Jan 11, 2017

$\int \frac{d x}{1 - x} = - ln | 1 - x |$ $int (dx)/(1-x) = -lnabs(1-x)$

Explanation:

Substitute:

$t = 1 - x$ $t= 1-x$
$d t = - d x$ $dt = -dx$

and you have:

$\int \frac{d x}{1 - x} = - \int \frac{d t}{t} = - ln | t | = - ln | 1 - x |$ $int (dx)/(1-x) = -int (dt)/t = -ln abs (t) = -lnabs(1-x)$

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