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∫−∞∞cosx1+x2 dx\large \int_{-\infty}^{\infty} \dfrac{\cos x}{1+x^{2}} \, dx∫−∞∞1+x2cosxdx
Find the value of the closed form of the above integral. Give your answer to 3 decimal places.
Bonus:
Solve this question without using contour integration.
Generalise ∫−∞∞cos(x)a2+x2dx\displaystyle \int_{-\infty}^{\infty} \dfrac{\cos(x)}{a^{2}+x^{2}} dx∫−∞∞a2+x2cos(x)dx, where aaa is a constant.
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