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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?