AngouriMath
SolveByWritingAPowerOfAMultipleOfXAsAPowerOfX(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A factor (c x)^t of the integrand, t not whole, written as x^t with
(c x)^t x^(-t) in front: Rubi's (c x)^(-1 - 2 n - n p) (a + b x^n)^p and
(d x)^(-1 - 2 n (1 + p)) (a^2 + 2 a b x^n + b^2 x^(2 n))^p , whose powers of x alone are
answered.
answered.
Remarks
The derivative of (c x)^t x^(-t) is t (c x)^t x^(-t) (c/(c x) - 1/x) , zero
wherever it is defined, since(c x)^(t - 1) is (c x)^t/(c x) for the principal
power: it is a constant on each interval of the domain, for either sign of c and of x, and
goes in front of the integral of the rest. SolveByDistributingAPowerOfAMonomial(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) writesc^t x^t for a positive c only, and reads (c x^n)^t for an n that is
not whole. Late and at the question asked, so that a rule reading(c x)^t as
written goes first; the answer is differentiated back at sampled points.
https://github.com/asc-community/AngouriMath/issues/233
wherever it is defined, since
power: it is a constant on each interval of the domain, for either sign of c and of x, and
goes in front of the integral of the rest. SolveByDistributingAPowerOfAMonomial(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean) writes
not whole. Late and at the question asked, so that a rule reading
written goes first; the answer is differentiated back at sampled points.
https://github.com/asc-community/AngouriMath/issues/233
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