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## Homework Statement

Calculate ∫1/(x^2-1)dx from 2 to positive infinity. (Hint: You will need to write the antiderivative as a single logarithm in order to be able to calculate the appropriate limit.)

## Homework Equations

## The Attempt at a Solution

What I have so far is the following:

First re-writing as a limit->

lim ∫1/(x^2-1)dx from 2 to T

T->infinity

then using partial fractions

lim 1/2∫1/(x-1)dx - 1/2∫1/(x+1)dx from 2 to T

T->infinity

lim 1/2*ln|x-1| - 1/2*ln|x+1| from 2 to T

T->infinity

re-writing as a single natual log

lim 1/2*ln((x-1)/(x+1)) from 2 to T

T->infinity

now subtracting the endpoints

lim 1/2*ln((T-1)/(T+1)) - 1/2*ln(1/3)

T->infinity

now here is where i got a little confused again. T is approaching infinity but because we are taking a limit i can say that the first term is siply 1/2 correct? and the second remains 1/2*ln(1/3)? So i'm getting for my answers (exact and then approx):

1/2 - 1/2*ln(1/3) or approx 1.0493

Now I could be completely wrong and that is why I can't seem to get comfortable with these things. Can anyone shed some light on what I'm doing wrong, or perhaps right?

Thanks

-Mike