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(Solved): Complex Analysis/Variable Complex Using the residual method, calculate the following integral 3). ...
Complex Analysis/Variable Complex
Using the residual method, calculate the following integral 3). \( \int_{-\infty}^{\infty} \frac{x d x}{\left(x^{2}+1\right)\left(x^{2}+4\right)} \) 4). \( \int_{0}^{\infty} \frac{d x}{\left(x^{2}+4\right)^{2}} \)
Expert Answer
Explanation: To evaluate the integral [\int_{-\infty}^{\infty} (x^2 + 1)(x^2 + 4)x , dx,] we can try to find an antiderivative of the integrand that h