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RootSum

WMA link

RootSum[f, form]

sums form[x] for all roots of the polynomial f[x].

Integrating a rational function of any order:

• • Integrate[1/(x^5 + 11 x + 1), {x, 1, 3}]

• • N[%, 50]

Simplification of RootSum expression

• • RootSum[#^5 - 11 # + 1 &, (#^2 - 1)/(#^3 - 2 # + c) &]

• • RootSum[#^5 - 3 # - 7 &, Sin] //N//Chop

Use Normal to expand RootSum:

• • RootSum[1+#+#^2+#^3+#^4 &, Log[x + #] &]

• • %//Normal