0
∫1/(1-x)2dx
We can rewrite the integral as ∫(1-x)-2dx.
Thus:
∫(1-x)-2dx
u = 1-x
du = -1
-1∫-1(1-x)-2dx
-1∫u-2du
(u-1|0u=1-x
(1-x)-1
So we conclude that ∫1/(1-x)2dx = (1-x)-1 or 1/(1-x)
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