- #1

greentea

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## Homework Statement

Derive x/(1-x)

## Homework Equations

By substitution:

u = (1-x)

du = -dx

∫x/(1-x)dx = -∫(1-u)/u du = ∫1-(1/u)du = u-log(u)+c = (1-x) - log(1-x) + c

By decomposition:

x/(1-x) = 1/(1-x)-1

∫1/(1-x)-1dx = -log(1-x)-x+c

## The Attempt at a Solution

Which solutions should I use (1-x) - log(1-x) + c or -log(1-x)-x+c, or are both equally good?