Question

-dx neif a> 0 5. (a) x2+1 (b) For any real number a > 0, cos x dx ne"/a. a Hint: This is the real part of the integral obtained by replacing cos x by e

please prove part (b) use complex analysis and calculus of residue

Answer 1

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The last equation in first page is equation number (4).Finally we consider as R tends to infinity because we choose the radius R arbitrarily.