Explain the following integral:
$integral subscript 2 superscript 3 fraction numerator straight x over denominator straight x squared plus 1 end fraction dx$

Solution

Let I = $integral subscript 2 superscript 3 fraction numerator straight x over denominator straight x squared plus 1 end fraction dx space equals space 1 half integral subscript 2 superscript 3 fraction numerator 2 straight x over denominator straight x squared plus 1 end fraction dx space equals space 1 half left square bracket log left parenthesis straight x squared plus 1 right parenthesis right square bracket subscript 2 superscript 3 space space space$
$equals space 1 half left parenthesis log space 10 space minus space log space 5 right parenthesis space equals space 1 half log open parentheses 10 over 5 close parentheses space equals space 1 half log 2$

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Integrals

Explain the following integral:
$integral subscript 2 superscript 3 fraction numerator straight x over denominator straight x squared plus 1 end fraction dx$

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