= Gauss-Laguerre quadrature
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For the weight $e^{-x}$ on $[0,\infty)$, use the zeros of a degree-$n$ <Laguerre polynomial> as quadrature nodes. Divide a polynomial of degree at most $2n-1$ by that polynomial. The quotient term integrates to zero by orthogonality and vanishes at every node; interpolation of the remainder proves exactness. The two-node rule has nodes $2\pm\sqrt2$ and corresponding weights $(2\pm\sqrt2)/4$, with the larger weight at the smaller node.
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