(35S) Quick integration

[Albert Chan]

We can take advantage of odd/even function:

∫((5*x^3-3*x) * (x^2+p*x+q), x=-1 .. 1)      // odd function * even function = odd function
= ∫((5*x^3-3*x) * (p*x), x=-1 .. 1)               // odd function * odd function = even function
= 2p * ∫(5*x^4 - 3*x^2, x=0 .. 1)       
= 2p * (5/5 - 3/3)
= 0

This explained coefficients (5, -3) for Gaussian quadrature 3-points abscissa

(5*x^3-3*x) = 5*x*(x^2-0.6) = 0      → x = 0, ±√(0.6)