Question: How to speed up the calculation of the double integral?

I want to calculate the double integral of the following expression which includes sum of several Legendre polynomial terms, but the speed is so low. Any suggestion to speed up the calculation?

NULL

Restart:

NULL

II := 9:

JJ := 9:

M := 9:

NULL

`ΔP1` := add(add(add(add(add(add(add(-(LegendreP(i, zeta__1)*LegendreP(j, eta__1)*(diff(diff(tau[r](t), t), t))+LegendreP(m, zeta__1)*LegendreP(j, eta__1)*(diff(tau[r](t), t))+LegendreP(m, zeta__1)*LegendreP(j, eta__1)*tau[r](t))/sqrt(LegendreP(m, zeta__1)*LegendreP(j, eta__1)+LegendreP(i, zeta__1)*LegendreP(l, eta__1)), i = 1 .. II), j = 1 .. JJ), k = 1 .. II), m = 1 .. II), l = 1 .. JJ), n = 1 .. JJ), r = 1 .. M):

A := int(int(`ΔP1`, zeta__1 = -1 .. 1), eta__1 = -1 .. 1):

A

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