Integrating Problem: Definite Integral from sqrt2 to 2

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The discussion centers on evaluating the definite integral of the function 1/(x^3√(x^2-1)) from √2 to 2. The user has attempted to separate the integrand into two parts, using trigonometric substitution for the second part, and is uncertain about the integration of 1/x^3. There is a suggestion that the entire integrand can be simplified more effectively with a single trigonometric substitution rather than separating it. Clarification is requested regarding the user's method, indicating some confusion about the integration process. The conversation highlights the importance of a cohesive approach to solving the integral.
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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?
 
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miller8605 said:
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?
 

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