Evaluate the definite integral:
$integral subscript 2 superscript 3 fraction numerator 1 over denominator straight x squared minus 1 end fraction dx$

Solution

Let I = $integral subscript 2 superscript 3 fraction numerator dx over denominator straight x squared minus 1 end fraction space equals space 1 half open square brackets log space open parentheses fraction numerator straight x minus 1 over denominator straight x plus 1 end fraction close parentheses close square brackets subscript 2 superscript 3$
$equals space 1 half open square brackets log space open parentheses fraction numerator 3 minus 1 over denominator 3 plus 1 end fraction close parentheses minus log space open parentheses fraction numerator 2 minus 1 over denominator 2 plus 1 end fraction close parentheses close square brackets space equals space 1 half open parentheses log space 1 half minus log space 1 third close parentheses equals space 1 half log open parentheses 1 half cross times 3 over 1 close parentheses space equals space 1 half log 3 over 2$

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Integrals

Evaluate the definite integral:
$integral subscript 2 superscript 3 fraction numerator 1 over denominator straight x squared minus 1 end fraction dx$

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