find the integral of 1/(t^3(t^2-1)^1/2))
I tried this a multiple of times by treating u as secu. But somehow, the answer ends up as arctan something.
Note that your integral is the same as:
Now, let , the integral becomes:
The first integral will give you your arctan. For the second integral, use an appropriate trig sub.
You should end up with the desired antiderivative.