AngouriMath
SolveAPowerOfXTimesAHyperbolicFunctionOfAPowerUnderThatPower(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A power of x times a rational function of hyperbolic functions of a linear in a whole
power of x,x^m F(sinh(c + d x^n), cosh(c + d x^n)) with n >= 2 dividing
m + 1 , under t = x^n : x^m dx is t^(k - 1) dt/n for
k = (m + 1)/n , and the question in t is the same function of a linear in
t beside a whole power of t .
power of x,
Remarks
The library writes the hyperbolic functions as exponentials, so x sech(a + b x^2)^7 arrives as x beside a seventh power of a quotient of exponentials of a + b x^2 , and
the rules before this one spent the budget on it: Rubi's 6.5.2 and 6.6.2
x sech(a + b x^2)^7 , x/(a + b sech(c + d x^2))^2 and the two with the
cosecant, 6.1.3 and 6.2.3sinh(a + b x^2)^3/x^3 and its cosine, and 6.7.1
x^5 cosh(a + b x^3)^7 sinh(a + b x^3) , each of which in t is answered in
under a second. Exact wherever the integrand is defined, since the powers are whole:
x^m is x^(n - 1) (x^n)^(k - 1) at every x but 0. Exponentials of a
linear inx^n and whole powers of them only, with a whole power past the first of
a sum or a quotient of them among them:x/(a + b sech(c + d x^2)) and
x^3 sinh(a + b x^2) are answered as written, in fewer characters than in
t , and are left to that. After the rules that answer a polynomial beside
exponentials of a quadratic as written, which it leaves as they were; a symbolic
n is SolveByAPowerOfTheVariableTimesAFunctionOfItsPower(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)'s.
https://github.com/asc-community/AngouriMath/issues/233
the rules before this one spent the budget on it: Rubi's 6.5.2 and 6.6.2
cosecant, 6.1.3 and 6.2.3
under a second. Exact wherever the integrand is defined, since the powers are whole:
linear in
a sum or a quotient of them among them:
exponentials of a quadratic as written, which it leaves as they were; a symbolic
https://github.com/asc-community/AngouriMath/issues/233
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