AngouriMath
OverTheLeastPowersOfTheSineAndTheCosine(AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity@)
Method (no overloads)
Summary
power of each times the sum of what is left;
is not such a product.
Remarks
What parts leaves is spelled the way the antiderivative came back, and the other
terms the way they were written:(1/sin(x))^(-1/2) beside
sqrt(csc(x)) sec(x) tan(x) share nothing as written, and are
sqrt(sin(x)) and sqrt(sin(x))/cos(x)^2 as powers. Reading
(1/f)^p as f^(-p) holds wherever f is positive or p is
whole; where neither, the integrand is not real.
And antiderivative where the sum is the derivative of one such
product, which the rules otherwise answer in the half angle's tangent at four times
the size:(K sin(u)^(a + 1) cos(u)^(b + 1))' is
K u' sin(u)^a cos(u)^b ((a + b + 2) cos(u)^2 - (b + 1)) , and
K u' sin(u)^a cos(u)^b ((a + 1) - (a + b + 2) sin(u)^2) the other way, so
sqrt(sin(x)) (-2 - 4/cos(x)^2) is (-4 sin(x)^(3/2)/cos(x))' .
terms the way they were written:
whole; where neither, the integrand is not real.
product, which the rules otherwise answer in the half angle's tangent at four times
the size:
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