# Integral of 2/(x^2-1)dx HELP

1. Oct 30, 2011

### masonm127

Integral of 2/(x^2-1)dx HELP!!!

1. The problem statement, all variables and given/known data

Evaluate: ∫2/(x2-1)dx

2. Relevant equations
Inverse trig functions arent working.
∫1/x+1dx=ln(1+x)

3. The attempt at a solution

My tutor and i both attemped the solution many ways, and are still at a stand still.
According to my calculator and wolfram alpha, the answer is -ln(x+1/x-1)
The closest i have gotten is 2∫$1/((x+1)(x-1))$dx

2. Oct 30, 2011

### Dick

Re: Integral of 2/(x^2-1)dx HELP!!!

Did you try using partial fractions?

3. Oct 30, 2011

### ArcanaNoir

Re: Integral of 2/(x^2-1)dx HELP!!!

if you multiply by -1 I think you can use tanh^-1

4. Oct 30, 2011

### masonm127

Re: Integral of 2/(x^2-1)dx HELP!!!

Thanks! partial fractions worked! didn't even think about that. the solution came out to be -ln(x+1)+ln(x-1), which is apparently equal to -ln((x+1)/(x-1))

5. Oct 30, 2011

### ArcanaNoir

Re: Integral of 2/(x^2-1)dx HELP!!!

and also apparently equal to tanh^-1

6. Oct 30, 2011

### masonm127

Re: Integral of 2/(x^2-1)dx HELP!!!

The full question is to find the integral over infinity and 2, so i have to use limits. im getting an undefined answer since ln of infinity minus ln infinity is undefined. does that sound right?

7. Oct 30, 2011

### Dick

Re: Integral of 2/(x^2-1)dx HELP!!!

Not right. You should really be writing things like the integral of 1/(1+x) as log(|1+x|). Since it's an improper integral, to work out the infinity part of your limit you need to think about the limit as x->infinity of log(|1+x|/|1-x|). What's that?

8. Oct 30, 2011

### masonm127

Re: Integral of 2/(x^2-1)dx HELP!!!

should be zero right? Not used to using log to write things, its just something our teacher never really told us to do. makes sense though

9. Oct 30, 2011

### Staff: Mentor

Re: Integral of 2/(x^2-1)dx HELP!!!

Although my choice would be partial fractions decomposition, a trig substitution will also work here, with secθ = x, secθtanθdθ = dx. The resulting integral is
$$2\int csc\theta d\theta$$