Could anybody integrate this without using methods from Complex Analysis?
$$ \int^{\infty}_{-\infty}\frac{x\sin x}{(x^2+a^2)(x^2+b^2)}dx $$
Could anybody integrate this without using methods from Complex Analysis?
$$ \int^{\infty}_{-\infty}\frac{x\sin x}{(x^2+a^2)(x^2+b^2)}dx $$
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.