In my homework there is a integral looks so strange, this is the first time that I see this kind of thing. So I have no idea what to do.
$\int_{0}^{-1+i\infty}(z+1)e^{iz}dz$
What does it mean the upper part of integral $-1+i \infty$? And how can i solve it?
I tried to take integral respect to $z$. Then i wrote $z=x+iy$ and put from $0$ to $-1$ for all x and put from $0$ to $\infty$ for all y. Am I right?
It is better to consider first $$I_p=\int_{0}^{-1+ip}(z+1)\,e^{iz}\,dz$$ Expandin the integrand, one integration by parts gives the antiderivative and using the bounds $$I_p=e^{-(p+i)} (p+1)-(1-i)$$ Now, take the limit when $p\to \infty$.