Question

integrate 1/t(t^2-1)^1/2

Answer 1

A long way would be to allow \(u=t^2-1\). This is awfully ugly and required integration by parts. Though, I'm sure there is a nicer way.

Answer 2

ok

Answer 3

cn u solve it completely

Answer 4

I mean, it can be solved completely, but I'm not going to write it all up. Here's the gist:
\[
\int_\gamma \frac{dt}{t\sqrt{t^2-1}}=\int_\gamma \frac{du}{(u-1)\sqrt{u}}
\]Do integration by parts on the last integral and you should get the answer.

Answer 5

That should be a \(u+1\), not \(u-1\).

Answer 6

Made a mistake, the integral is this:
\[
\int_\gamma \frac{dt}{t\sqrt{t^2-1}}=\frac{1}{2}\int_\gamma \frac{du}{(u+1)\sqrt{u}}
\]

Answer 7

ok i got it thanks

Answer 8

Easier method:

Let \(u=\sqrt{t^2-1}\)!