How would you take the integral of 1/ (x^2 - 1) from 2 to infinity. I tried by using partial fraction integration technique to simplify it to an ln function, but I am not sure what to do next.
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∫dx/(x² - 1) from 2 to ∞
1/2*∫1/(x - 1) - 1/(x + 1) dx
1/2*ln|(x - 1)/(x + 1)| eval. from 2 to ∞
lim b->∞ 1/2*ln|(b - 1)/(b + 1)| - 1/2*ln(1/3) = 1/2*ln(1) - 1/2*ln(1/3) = 1/2*ln(3)
= ln(√3)
1/2*∫1/(x - 1) - 1/(x + 1) dx
1/2*ln|(x - 1)/(x + 1)| eval. from 2 to ∞
lim b->∞ 1/2*ln|(b - 1)/(b + 1)| - 1/2*ln(1/3) = 1/2*ln(1) - 1/2*ln(1/3) = 1/2*ln(3)
= ln(√3)