Integrating lnx/(1+x²) from 0 to infinity: two methods

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∫ln(x)/(1 - x²) dx [0, 1]. Solve using Double Integrals method.∫ln(x)/(1 - x²) dx [0, 1]. Solve using Double Integrals method.
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Integral lnx/(1+x^2)^2 from 0 to infinityIntegral lnx/(1+x^2)^2 from 0 to infinity
∫ln(x)/(1 + x²) dx [0, ∞] = ? Fast solution of an interesting integration problem with logarithm.∫ln(x)/(1 + x²) dx [0, ∞] = ? Fast solution of an interesting integration problem with logarithm.