AngouriMath
SolveByTakingAFunctionOutOfASymbolicRootOfItsPower(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A power of a constant times a power of a function of x whose exponents multiply to a whole
number with a symbol in them, the function taken out:(c sin(u)^n)^(1/n) is
K sin(u) with K = (c sin(u)^n)^(1/n)/sin(u) , constant between the zeros of the
sine, carried through the integration as a symbol and written back. Rubi's 4.1.7 and 4.2.0
(c sin(a + b x)^n)^(1/n) , -cot(a + b x) (c sin(a + b x)^n)^(1/n)/b , was declined.
number with a symbol in them, the function taken out:
sine, carried through the integration as a symbol and written back. Rubi's 4.1.7 and 4.2.0
Remarks
For a real f of one sign on an interval, f^m is |f|^m times a constant
phase, soc f^m keeps its argument there and its principal power is
(c f^m)^r = K f^(m r) with K constant: the logarithmic derivatives of the two
sides are bothm r f'/f . The rule above reads numbers for the exponents and writes
the sign; a symbol leaves the constant as written, as Rubi does. Not of a polynomial, whose
powers the rules forx^m (a + b x^n)^p take apart. At the top only, as above.
https://github.com/asc-community/AngouriMath/issues/233
phase, so
sides are both
the sign; a symbol leaves the constant as written, as Rubi does. Not of a polynomial, whose
powers the rules for
https://github.com/asc-community/AngouriMath/issues/233
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