Evaluate the following definite integral:
$integral subscript 1 superscript 2 left parenthesis log space straight x squared right parenthesis dx.$

Solution

I = $integral subscript 1 superscript 2 left parenthesis logx squared right parenthesis space dx space space space space equals 2 space integral subscript 1 superscript 2 left parenthesis log space straight x right parenthesis. space space space 1 space dx space equals space 2 space open curly brackets open square brackets left parenthesis logx right parenthesis. straight x close square brackets subscript 1 superscript 2 minus integral subscript 1 superscript 2 1 over straight x. straight x space dx close curly brackets$
$equals space 2 left parenthesis 2 space log space 2 space minus space 1 space log space 1 right parenthesis space minus 2 integral subscript 1 superscript 2 1 space dx space equals space 2 left parenthesis 2 space log space 2 space minus 0 right parenthesis space minus space 2 open square brackets straight x close square brackets subscript 1 superscript 2 equals space 4 space log space 2 space minus 2 space left parenthesis 2 minus 1 right parenthesis space equals space 4 space log space 2 space minus space 2$

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Integrals

Evaluate the following definite integral:
$integral subscript 1 superscript 2 left parenthesis log space straight x squared right parenthesis dx.$

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