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Evaluate: int(logx)^2\ dx...

Evaluate: `int(logx)^2\ dx`

Text Solution

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We have given `int(logx)^2\ dx`
`I=int(logx)^2\ dx`
By Integrating by parts,
`I=x(logx)^2−2intx.logx.1/xdx`
`I=x(logx)^2-2intlogxdx`
`I=x(logx)^2-2[xlogx-x]+c`
`I=x[(logx)^2-2logx+2]+c`
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