Evaluate int(0)^(1) xlog(1+x)dx and henc...

Evaluate `int_(0)^(1) xlog(1+x)dx` and hence show that,
`(1)/(1xx3)-(1)/(2xx4)+(1)/(3xx5)-(1)/(4xx6)+..=(1)/(4)`

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The correct Answer is:

`(1)/(4)`

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