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Evaluate: int0^1x(tan^(-1)x)^2dx...

Evaluate: `int_0^1x(tan^(-1)x)^2dx`

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Given:`int_0^1x(tan^(-1)x)^2dx`
`I=int_0^1x(tan^(-1)x)^2dx`
`I=[(x^2)/2 (tan^(-1)x)^2]_0^1-int_0^1 (x^2)/2xx tan^(-1)x 1/(1+x^2) dx`
`I=(pi^2)/32-[tan^(-1)x(x-tan^(-1)x]_0^1+int_0^1 1/(1+x^2) (x-tan^(-1)x)dx`
`I=(pi^2)/32-pi/4+(pi^2)/16+int_0^1 x/(1+x^2)dx-int_0^1 (tan^(-1)x)/(1+x^2)dx`
`I=(pi^2)/32-pi/4+(pi^2)/16+[1/2log(1+x^2)]_0^1`
`I=(pi^2)/16-pi/4+1/2log2`
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