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The value of $\int_{0}^{\infty} \frac{x \log x}{{(1 + x^{2})}^{2}} d x$ is

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Correct option is A

Putting u=1/xI=∫0∞ xlog⁡x1+x2dx=∫∞0 ulog⁡u1+u22du=−ISo I =0.

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The value of ∫0∞ xlog⁡x1+x22dx is

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The value of $\int_{0}^{\infty} \frac{x \log x}{{(1 + x^{2})}^{2}} d x$ is