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


by aija
Tags: integrate
aija
aija is offline
#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.
Phys.Org News Partner Science news on Phys.org
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered
arildno
arildno is offline
#2
Dec4-12, 12:04 PM
Sci Advisor
HW Helper
PF Gold
P: 12,016
Try partial fractions decomposition, remembering that (x^2-1)=(x+1)(x-1)
Ray Vickson
Ray Vickson is offline
#3
Dec4-12, 12:23 PM
HW Helper
Thanks
P: 4,664
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).


Register to reply

Related Discussions
Integrate (2x^2+1)e^x^2dx (...Wow, seriously?) Calculus & Beyond Homework 3
Integrate 1/cos(x) Calculus & Beyond Homework 9
integrate dy/dx Calculus & Beyond Homework 9
How to integrate (x^2-1)^n Calculus & Beyond Homework 4