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2 problems match “residue theorem”. Clear

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1. Contour integral of 1/(z^2+1) ●●○○○ 20 ptsCompute the complex contour integral $\displaystyle\int_{|z|=2}\frac{1}{z^2+1}\,dz$, where the circle $|z|=2$ is traversed once counterclockwise.
2. Principal value with real poles ●●●○○ 50 ptsFind the Cauchy principal value of $\int_{-\infty}^{\infty}\frac{x\,dx}{(x-1)^4-1}$, where the poles at $0$ and $2$ lie on the real axis. Round to two decimal places.