AngouriMath
SolveAPowerOfALinearOverAPowerOfAQuadratic(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A power of a linear that is not whole, times a linear, over a whole power of a quadratic,
with the power of the quadratic lowered one at a time:
integral L^m N Q^p = (alpha + beta x) L^(m + 1) Q^(p + 1) + integral L^m W Q^(p + 1) for p <= -2 , where alpha and beta make
N - (alpha + beta x) (p + 1) L Q' a multiple of Q and
W = (N - (alpha + beta x) (p + 1) L Q')/Q - beta L - (alpha + beta x) (m + 1) e is
linear again; atp = -1 the integrator answers what is left.
with the power of the quadratic lowered one at a time:
linear again; at
Remarks
The derivative of the first term is L^m Q^p times
beta L Q + (alpha + beta x) (m + 1) e Q + (alpha + beta x) L (p + 1) Q' , which with
L^m Q^(p + 1) W added is L^m Q^p N . (alpha + beta x) L Q' modulo
Q is (alpha + beta x) (r1 x + r0) with r1 = 2 c d - b e and
r0 = b d - 2 a e , for L = d + e x and Q = a + b x + c x^2 , and
matching it toN is two equations in two unknowns. Rubi's 1.2.1.2
(d + e x)^(7/2)/(a + b x + c x^2)^2 ran past a minute and
sqrt(d + e x)/(a + b x + c x^2)^3 took thirty seconds for 26,437 characters.
https://github.com/asc-community/AngouriMath/issues/718
matching it to
https://github.com/asc-community/AngouriMath/issues/718
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