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I need to calculate the integration using Cauchy's Residue Theorem $$\int_{-\infty}^{\infty} \frac{x^2}{(x^2+1)(x^2+9)}dx$$

I am stuck here how can I approach this.

$$\int_{Cr}^{} f(z) dz = 0$$.

I need to show that the function is zero using Jordan's Lemma.

Ratul Das
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  • Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Oct 28 '21 at 04:22
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    Use the inequality $|\int_{\Gamma} f(z) dz|\le \max_{z\in\Gamma} |f(z)| \cdot \text{length}(\Gamma)$. – Just a user Oct 28 '21 at 04:31

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