Evaluate int x^(2)log (1-x^(2))dx, and ...

Evaluate `int x^(2)log (1-x^(2))dx`, and
hence prove that `(1)/(1.5)+(1)/(2.7)+(1)/(3.9)+...=2/3 log 2 - 8/9`.

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Verified by Experts

The correct Answer is:

`2/3 log (2)-8/9`

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