Repository navigation
Integrate a power of x beside a power of a logarithm of a binomial in that binomial - #2093
Merged
Rafael-SOWNet merged 1 commit intoOct 23, 2026
Merged
Conversation
… that binomial x^k beside a power that is not whole of a logarithm of one binomial a + b x^q is written in t = a + b x^q where N = (k + 1)/q is a whole number above 0. Then x^k dx is (t - a)^(N - 1) dt/(q b^N) on every branch, since x^(k + 1) = (x^q)^N and x^(k + 1 - q) = (x^q)^(N - 1) are whole powers of x^q, and the integrand in t is a polynomial beside the logarithm's power, which the rules answer: (a + b ln(c (d + e/sqrt(x))))^p/x^2 is -2/e^2 times the integral of (t - d) (a + b ln(c t))^p. An exponential of a binomial is left to the exponential rules, which write it in its own base. Part of #2075. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
Rafael-SOWNet
force-pushed
the
a-power-of-x-beside-a-function-of-a-binomial
branch
from
October 23, 2026 14:49
a0dd149 to
0a3790e
Compare
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Integrates
x^kbeside a power of a logarithm of one binomiala + b x^qby writing it int = a + b x^q. Part of #2075.The rule. Where
N = (k + 1)/qis a whole number above 0,x^k dxis(t - a)^(N - 1) dt/(q b^N). That holds on every branch, sincex^(k + 1) = (x^q)^Nandx^(k + 1 - q) = (x^q)^(N - 1)are whole powers ofx^q. The integrand intis then a polynomial beside the logarithm's power, which the rules answer. For example,(a + b ln(c (d + e/sqrt(x))))^p/x^2is-2/e^2times the integral of(t - d) (a + b ln(c t))^p.Only a power of a logarithm is taken. The first version took an exponential of a binomial too, and answered
f^(a + b/x)/x^4ase^(ln f (a + b/x)), where the exponential rules write it in its own base,f^(a + b/x). A test that pins that form failed.Measured on Rubi's suite, with the harness that reads
GAMMA, against68211405, the whole corpus each side. This branch sits on2be40bad, which adds #2088 to that base.68211405The gains are 3.4's 14 rows,
3.4:696-750. The other 5 are #2088's:6.1.1:205-207and6.1.3:98/100. Families 2 and 3 were run again after the narrowing, 2,274 rows: the same 14 gains, 0 wrong, 0 lost. Allocation per stream is 1.0002, 1.0001 and 0.9946 of the base's, and time 1.015, 1.026 and 0.922. One row's allocation grew in the run,6.1.7:196, which is the same alone on both builds (1.079 GB), as it was for #2088 and #2090.Three integrals differentiate back in the tests. The suite passes (16,955), and so do the MCP tests (329).
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura