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Integrate 1 / (x^2 - 1)^2

by aija
Tags: integrate
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aija
#1
Dec4-12, 12:01 PM
P: 15
1. The problem statement, all variables and given/known data
integrate dx / (x^2 - 1)^2


2. Relevant equations



3. The attempt at a solution
There is nothing i can substitute to get rid of x. Except x=sqr(t), but then dx is 1/2sqr(t) so i get:

∫( dt / (t-1)^2 * 2sqr(t) )

and it's still impossible to integrate.
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arildno
#2
Dec4-12, 12:04 PM
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P: 12,016
Try partial fractions decomposition, remembering that (x^2-1)=(x+1)(x-1)
Ray Vickson
#3
Dec4-12, 12:23 PM
Sci Advisor
HW Helper
Thanks
P: 5,086
Quote Quote by aija View Post
1. The problem statement, all variables and given/known data
integrate dx / (x^2 - 1)^2


2. Relevant equations



3. The attempt at a solution
There is nothing i can substitute to get rid of x. Except x=sqr(t), but then dx is 1/2sqr(t) so i get:

∫( dt / (t-1)^2 * 2sqr(t) )

and it's still impossible to integrate.
A more-or-less standard substitution to try out when you see 'x^2-1' is x = cosh(t).


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