sqrt(a + b sech(x)) tanh(x)^5 is integrated wrongly: the root of 1 - u^2 is written through the imaginary unit #1370

sqrt(a + b*sech(x))*tanh(x)^5 (Rubi 6.5.3:178, with x for c + d x) integrates on master (01fa27bb) to an answer beginning ((2i * i * -a^3 * (sqrt(a + i*b*sqrt(((e^(2x) - 1)/(e^(2x) + 1))^2 - 1)) ... whose derivative differs from the integrand by 0.41 relative at a = 1.37, b = 2.71, x = 0.31 (0.44 at 0.57, 0.26 at 0.83, 0.045 at 1.29).

Route: SolveByHyperbolicTangentSubstitution (a radicand of both signs, sech(x) being 2v/(v^2 + 1)), which writes sech(x) as w = sqrt(1 - u^2) and hands u^5 sqrt(a + b sqrt(1 - u^2))/(1 - u^2) on; a rule below writes sqrt(1 - u^2) as i sqrt(u^2 - 1), which on |u| < 1 -- the whole range of tanh -- is the wrong sign of the real root, the same class as the imaginary Euler substitution noted before.

The PR that found it (the hyperbolic tangent route for #718's family 6, which also taught this rule a linear argument and so met the c + d x form in the sample) checks the rule's answer at sampled points when a symbol is involved, so it is a decline now; the rewrite through i is what is left to find.