WhereTheDerivativeHoldsBeyondTheRadicand​(AngouriMath.​Entity,​AngouriMath.​Entity,​AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

Where the derivative of antiderivative is shown to be
integrand on the part of the line where radicand is
negative: at every point there of a spread along the line, compared as complex numbers,
or at every point there where the integrand is real; at two points or more where it is
real, and nowhere that it is real does it differ or have no value. An answer built
through the root of the radicand as a real u -- a sign of u read as one,
sqrt(u^2 w) as u sqrt(w) -- was conditioned on the radicand for that, and
beside a second root imaginary there the integrand is real there too:
sqrt(a + b t)/t^(3/2) for t < -a/b, a product of two imaginary roots.
Whether the identities still hold there depends on the signs, so it is measured rather
than assumed: (1 + sec(x))^(5/2) sqrt(cos(x)) under u = sqrt(cos(x)) was the
integrand's negative wherever the cosine is negative, and sqrt(a + b t)/t^(3/2) under u = sqrt(t) is its antiderivative beyond t = -a/b and not between
-a/b and 0, where the integrand is imaginary.