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(a c + b c x)^(-3 - 2p) (f + g x) (a^2 + 2 a b x + b^2 x^2)^p is answered with an expression that has no value anywhere #1793
Description
(a*c + b*c*x)^(-3-2*p)*(f + g*x)*(a^2 + 2*a*b*x + b^2*x^2)^p, Rubi's 1.2.1.3:2459, integrates on master 113ae13b to an answer with the factor -(1/b * a * b * c - a * c)^(-2) in it, which is zero to the power -2: the answer has no value at any point. With exact parameters, a = 13/10, b = 7/10, c = 11/10, f = 3/10, g = 17/10, p = 2/7, its derivative at x = 57/100 and 129/100 is NaN at 50, 300 and 2000 digits, where the integrand is 0.18409... and 0.16590.... 2.5.0 declines it.
The square is written as a power of its root, (x + a/b)^(2p), beside a c + b c x, which is b c (x + a/b): one linear twice. SolveTwoLinearPowersWhoseExponentsSumToAWholeNumber divides by the cross term of its two linears, a/b (b c) - a c, and declines where that is zero, but tests it as a number, and with symbols in it, it is not one. (x + a/b)^(2*p)*(a*c + b*c*x)^(-3-2*p)*(f + g*x) alone shows it the same way.
Part of #233.
🤖 Generated with Claude Code
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