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

An exponential of a linear times half-odd powers of a hyperbolic sine of another linear, and the
cosine to the first power beside them, as the derivative of the same kind of sum: with
E = e^(a + b x), S = sinh(u), C = cosh(u) and u = c + d x,
(E S^p C^q)' = E (b S^p C^q + d p S^(p - 1) C^(q + 1) + d q S^(p + 1) C^(q - 1)), with
C^2 = 1 + S^2, so F is a sum of E S^p C^q over the integrand's monomials and their
partners, and its coefficients a linear system. Rubi's 6.7.1
e^(a + b x) sinh(c + d x)^(3/2) - 3/4 e^(a + b x) d^2/((b^2 - 9/4 d^2) sqrt(sinh(c + d x))) is (e^(a + b x) (b sinh^(3/2) - 3/2 d cosh sinh^(1/2))/(b^2 - 9/4 d^2))', where each term
alone is not elementary and the split declined both. Powers of one sine multiply on every
branch, and no power of a power is taken. Checked by its derivative.
https://github.com/asc-community/AngouriMath/issues/718