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Originally Posted by Random Variable If then . So the integral from 0 to is half the integral from 0 to . Next, f(x) is the real part of . Put . Then the integral becomes (integral round the unit circle), which you can evaluate by the residue theorem. (I make the answer .)
It's not as nice as Opalg's solution, but how about the following: Let now assuming it's OK to differentiate inside of the integral with respect to so which means that is independent of the value of to find let then and
Originally Posted by Random Variable It's not as nice as Opalg's solution, but how about the following: Let now assuming it's OK to differentiate inside of the integral with respect to so which means that is independent of the value of to find let then and That is cool.
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