# Evaluate integral of 2/(x^2-1) with respect to x

Since is constant with respect to , move out of the integral.
Factor the numerator and denominator of .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Write the fraction using partial fraction decomposition.
Simplify.
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
Since is constant with respect to , move out of the integral.
Let . Then . Rewrite using and .
Let . Find .
Differentiate .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Rewrite the problem using and .
The integral of with respect to is .
Since is constant with respect to , move out of the integral.
Let . Then . Rewrite using and .
Let . Find .
Differentiate .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Rewrite the problem using and .
The integral of with respect to is .
Simplify.
Substitute back in for each integration substitution variable.
Replace all occurrences of with .
Replace all occurrences of with .
Simplify each term.
Combine and .
Combine and .
Combine the numerators over the common denominator.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate integral of 2/(x^2-1) with respect to x

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