How can I evaluate $$\int_0^{\infty}\frac{x\sin(bx)}{x^2+1}dx \quad(b>0)$$ using residue calculus? I tried computing the residue of $\int_0^{\infty}\frac{z\exp(ibz)}{z^2+1}dz$ at $z=i$ and taking the imaginary part of it, but what contour should I use so that only the integral over the real axis is left?
2026-03-27 23:40:55.1774654855
Choosing a contour for residue integral
73 Views Asked by user660166 https://math.techqa.club/user/user660166/detail AtRelated Questions in INTEGRATION
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