Copied Evaluate the integrals \[ \int _{-\infty }^{\infty }\frac {\sin x}{x}\,dx, \] \[ \int _0^\infty \frac {x^\alpha }{x+1}\,dx. \] Raw LaTeX Evaluate the integrals \begin{enumerate} \item[(a)] \[ \int_{-\infty}^{\infty}\frac{\sin x}{x}\,dx, \] \item[(b)] \[ \int_0^\infty\frac{x^\alpha}{x+1}\,dx. \] \end{enumerate} Topic Tags Cauchy Integral Formula and Integral Theorems Fourier Transform and Sampling Theory Linear Programming and Optimization Real Integral Evaluation by Complex Methods