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InTermsOf​(AngouriMath.​Entity,​AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​AngouriMath.​Entity.​Variable)

 Method (no overloads)

Summary

expr written in terms of uSub, where that stands
for u.

Remarks

Ordinarily that is a plain substitution: the candidate occurs in the integrand, and
replacing it is all that is wanted.
A power of the variable is the exception, and it is the one that mattered. Substituting u = x^2 into x / (x^4 + 1) replaces nothing, because
x^4 is not written as (x^2)^2 and a substitution matches what is
written. So the integrand kept its x, the candidate was rejected, and
int x / (x^4 + 1) came back unevaluated while int x^3 / (x^4 + 1) —
whose substitution does occur — did not.
#233 So a power substitution rewrites the other powers of the variable into powers of
itself. For u = x^r the identity is x^n = u^(n/r), and the rewrite is
made wherever n/r is a whole number — which for a whole r means
r divides n, and is the only case this covered at first.
A fractional r is the case that reaches the other way, and it is what
int sqrt(x)/(1 + x^2) needs. There u = sqrt(x), so r is
1/2 and n/r is 2n — a whole number for every n, including
the bare x that a whole r can never rewrite. The integrand becomes
2u^2/(1 + u^4), which is answered.
 Nothing is assumed by it: the caller still checks that no x survives, so a
rewrite that does not clear the variable leaves the candidate rejected as before.

























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