Evaluate the following definite integral
$integral subscript 0 superscript 1 fraction numerator 2 straight x over denominator 5 straight x squared plus 1 end fraction dx$

Solution

Let I = $integral subscript 0 superscript 1 fraction numerator 2 straight x over denominator 5 straight x squared plus 1 end fraction dx space equals space 1 fifth integral fraction numerator 10 straight x over denominator 5 straight x squared plus 1 end fraction dx space space$
$equals space 1 fifth left square bracket log left parenthesis 5 straight x squared plus 1 right parenthesis right square bracket subscript 0 superscript 1 space equals space 1 fifth left square bracket log space 6 space minus log space 1 right square bracket space equals space 1 fifth log 6$

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Integrals

Evaluate the following definite integral
$integral subscript 0 superscript 1 fraction numerator 2 straight x over denominator 5 straight x squared plus 1 end fraction dx$

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