[Calculus] Bypassing Cyclic Integration by Parts
By: Tao Steven Zheng (鄭濤)
【Problem】
Use the integral
to compute and
simultaneously.


【Solution】
Since ,
Multiply the numerator and denominator by the complex conjugate on the right hand side.
By matching real terms and complex terms, and tacking on the arbitrary constant from integrating, we can conclude that
and

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