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I am attempting to evaluate the following integral: $$\int_0^\infty \frac{(ln(x))^2 }{1+x^2}dx$$

Using the substitution $x=e^u$ and $dx=e^u du$, I get: $$\int_{-\infty}^\infty \frac{u^2}{e^{-u} + e^u} du$$

It's suggested that I evaluate this integral in the complex plane. How do I complete this problem?

The problem is found in Arfken.


marked as duplicate by Ron Gordon calculus Dec 10 '15 at 19:28

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