3/2(1/(x+i)+1/(x-i))+5(-1/(x+i)+1/(x-i))/2i
3/2log(x+i)+3/2log(x-i)-5i/2(-log(x+i)+log(x-i))
(3/2+5i/2)log(x^2+1)-5ilog(x-i)
log(x-i)=log(x^2+1)^.5e^i(2pi-arctan1/x)
=.5log(x^2+1)+i(2pi-arctan(1/x))
=3/2log(x^2+1)+5arctan1/x+10pi