Now, I'm really tempted to use arcsin, but the denominator isn't a radical, so how do I deal with 1/1-u^2 ?
it's not "difference of squares" it's "partial fractions".
suppose we want to write this as:
.
then:
that is:
.
this means that:
A + B = 1
B - A = 0
we can solve this for A and B:
2B = 1 --> B = 1/2 --> A = 1/2. thus the 2 goes on the bottom.