Question

Please help me finish evaluating the following integral (click to see).

Answer 1

\[\int\limits_{3}^{\inf}\frac{ 2 }{ x^2-1 }dx\]
note: inf = infinity
this is where i am stuck
\[\lim_{t \rightarrow \inf} [\ln|\frac{ t-1 }{ t+1 }|-\ln|\frac{ 1 }{ 2 }|]\]

Answer 2

Note that \infty is \(\infty\)

Answer 3

ok thanks, i didn't know that and I couldn't find it in the equation editor.

Answer 4

To take infinite limits, divide everything by the highest degree term.

Answer 5

In this case, it is \(t\)

Answer 6

\[
\frac{t-1}{t+1} = \frac{t-1}{t+1}\cdot \frac{\frac{1}{t}}{\frac{1}{t}}= \frac{1-\frac{1}{t}}{1+\frac{1}{t}}
\]

Answer 7

I'm assuming that you integrated correctly.

Answer 8

\[\lim_{t \rightarrow \infty} [\ln(1)-\ln \frac{ 1 }{ 2 }]\]

Answer 9

\[t+1/t+1 - 2/t+1\]

Answer 10

=ln(2)