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How can you evaluate the following integral using residues? $$\int\limits_0^\infty\frac{\ln x}{\left(x^2+4\right)^2}\text{d}x$$

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marked as duplicate by ThePortakal, tired, Nosrati, Community Sep 7 '17 at 17:38

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  • $\begingroup$ Replace $\log(x)$ by $\log^2(x)$ and integrate the resulting function around a keyhole contour in complex plane $\endgroup$ – tired Sep 7 '17 at 17:30