Copied Evaluate the integrals: \[ I=\int _0^\infty \frac {\sin x}{x}\,dx, \] \[ I=\int _0^\infty \frac {x^\alpha }{2+x}\,dx \qquad (-1<\alpha <1). \] Raw LaTeX Evaluate the integrals: \begin{enumerate} \item[(a)] \[ I=\int_0^\infty \frac{\sin x}{x}\,dx, \] \item[(b)] \[ I=\int_0^\infty \frac{x^\alpha}{2+x}\,dx \qquad (-1<\alpha<1). \] \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