AngouriMath
SolveAsXTimesARationalFunctionOfAnExponentialOfALogarithm(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
x times a rational function of an exponential whose exponent has a constant Euler
derivative,x g'(x) = c , read off the integrand: Rubi's 6.5.3
(1 - b^2 n^2) sech(u) + 2 b^2 n^2 sech(u)^3 for u = a + b ln(c x^n) is
(x (-sech(u) - b n tanh(u) sech(u)))' , and was declined.
https://github.com/asc-community/AngouriMath/issues/233
derivative,
https://github.com/asc-community/AngouriMath/issues/233
Remarks
With w = e^g , x w' = c w , so (x G(w))' = G + c w G'(w) : the integrand
P/Q in w is that for G = N/Q exactly where
N Q + c w (N' Q - N Q') = P Q , linear in N's coefficients and read at sampled values
of w. A symbolic c makes the solution unique, the homogeneous one beingw^(-1/c) . Only
where x stands in the exponentials alone, the others whole powers of the first, and checked.
of w. A symbolic c makes the solution unique, the homogeneous one being
where x stands in the exponentials alone, the others whole powers of the first, and checked.
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