Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 7D (Further Complex Methods)

The ordinary integral fails because the simple real poles at $-2$ and $3$ produce nonintegrable logarithmic singularities. Partial fractions giveClosing above for $\omega >0$ and below for $\omega <0$, with symmetric semicircular indentations, yieldsTaking real and imaginary parts,All integrals here run over $\mathbb{R}$.