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

  • Thread starter aija
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  • #1
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Homework Statement


integrate dx / (x^2 - 1)^2


Homework Equations





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.
 

Answers and Replies

  • #2
arildno
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Try partial fractions decomposition, remembering that (x^2-1)=(x+1)(x-1)
 
  • #3
Ray Vickson
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Homework Statement


integrate dx / (x^2 - 1)^2


Homework Equations





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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