Could anybody integrate this without using methods from Complex Analysis?
$$ \int^{\infty}_{-\infty}\frac{x\sin x}{(x^2+a^2)(x^2+b^2)}dx $$
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3Write $$h(\omega) = \int_{-\infty}^\infty \frac{x\sin (\omega x)}{(x^2+a^2)(x^2+b^2)},dx$$ and recognise a(n inverse) Fourier transformation (modulo constants). [I'm not saying that is necessarily easy, I'd use the residue theorem.] – Daniel Fischer Oct 01 '14 at 20:20
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One approach would be to use partial fraction decomposition, in conjunction with differentiation under the integral sign, since $\dfrac d{da}\cos(ax)=-x\sin(ax)$. Then check out the many answers to this question, and try to imitate them.
