Evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2dx}{x^2-1},$ for $x>1,$ in two ways: using partial fractions and a trigonometric substitution. Reconcile your two answers.

Fist evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2dx}{x^2-1}$ using partial fractions. Factor the denominator of the integrand.

$x^2-1=$

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