(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

show that the integral of z^i dz from -1 to 1 is equal to (1+e^(-pi))/x * (1-i)

where the path of integration is any contour from -1 to 1 above the x axis

2. Relevant equations

3. The attempt at a solution

I wrote z^i as e^iLogz and I think all I really need to do is find the antiderivitive of e^i*logz where -pi/2<argz<3pi/2

this antiderivative is giving me trouble I tried to break it up into e^i*lnr-theta

and then get -e^(i*lnr)*[e^(3pi/2)-e^(-pi/2)] but I can't get it to work

can anyone help?

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# Path of integration

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