AngouriMath
SolveByTakingAFunctionOutOfAPowerOfItsEvenPower(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A fractional power of a constant times an even power of a function of x, the
function taken out of the power with its sign:(a sin(x)^2)^(5/2) is
a^(5/2) |sin(x)|^5 , which is a^(5/2) sgn(sin(x)) sin(x)^5 -- the sign
a constant between the sine's zeros, carried through the integration as a symbol
and written back. Rubi'sx sqrt(sin(x)^2) is sgn(sin(x)) (sin(x) - x cos(x)) that way, and 1/(csc(x)^2)^(7/2) is sgn(csc(x)) times the seventh power
of the sine, where the substitutions read the root of the square as a modulus and
answered in powers of it.
function taken out of the power with its sign:
a constant between the sine's zeros, carried through the integration as a symbol
and written back. Rubi's
of the sine, where the substitutions read the root of the square as a modulus and
answered in powers of it.
Remarks
An even power of a real function is not negative, so (c q)^p = c^p q^p holds
for the principal powers whateverc is, and (f^(2k))^p is |f|^(2kp) .
Whole products of the exponents only, so that what is handed on is a whole power of
the function; a polynomial radicand is the rule above's, which comes first. At the
top only, as there: a substitution's variable is one it knows the sign of, and a
sign written for it is one nothing differentiates.
https://github.com/asc-community/AngouriMath/issues/718
for the principal powers whatever
Whole products of the exponents only, so that what is handed on is a whole power of
the function; a polynomial radicand is the rule above's, which comes first. At the
top only, as there: a substitution's variable is one it knows the sign of, and a
sign written for it is one nothing differentiates.
https://github.com/asc-community/AngouriMath/issues/718
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