>>355
I(x)=∫x*e^x*exp(ix) dx
= ∫x*exp{(i+1)x} dx
= x/(i+1)*exp{(i+1)x} -1/(i+1)*∫exp{(i+1)x} dx (部分積分)
= x/(i+1)*exp{(i+1)x} -1/(i+1)^2*exp{(i+1)x}
= x(1-i)/2*exp{(i+1)x} -{(1-i)/2}^2*exp{(i+1)x}
= 1/2*e^x*{ x(1-i)*exp(ix) + i*exp(ix) }

(与式) = Im{I(x)}
= 1/2*e^x*{ x*sin(x) -x*cos(x)) +cos(x) }
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