OpenType MATH Fonts

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We note that $x\mapsto \mathrm{\Im }\left(f\left(x\right)\right)$ is the integrand above. We also note that the poles of $f$ are $z^{\pm }=-1\pm 2i$. By choosing the right contour, one can show that and thus $${\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{16\sin \left(2x+\pi \right)}{5{\left(x^2+2x+5\right)}^2}dx=\frac{\pi \sin \left(2\right)}{e^4}$$