What is the integral of 1 over 1 minus x squared?

Answer 1

∫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)