Integrating Problem: Definite Integral from sqrt2 to 2

[miller8605]

Homework Statement

i'm taking a defitinite integral from sqrt2 to 2 of the function 1/x^3*sqrt(x^2-1)dx.

Homework Equations

The Attempt at a Solution

I separated it into 1/x^3 and 1/sqrt(x^2-1). I have the second part using trig sub. as being sec theta dtheta, before integrating it. I believe i did this part correctly.

What I can't remember is that I make 1/x^3 to x^-3 and then integrate it that way with the final being -1/2(1/x^2)??

Am i going about this correctly?

 

[quantumdude]

I separated it into 1/x^3 and 1/sqrt(x^2-1).

No need to do that. The entire integrand comes out very nice with a trig substitution.

I have the second part using trig sub. as being sec theta dtheta[/color], before integrating it. I believe i did this part correctly.

The part in red[/color] makes very little sense to me, but it sounds like it has the kernel of a correct method in there. Could you elaborate?