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Unexpected result using Integrate

Artur Jasinski, Grafix
Posted 10 days ago 
(-1) Integrate[Log[1 + Sqrt[1 - x]] Log[1 - x]/x, {x, 0, 1}]

Mathematica give 0

but should be

3 Zeta[2] Log[2] - 9 Zeta[3]/4
POSTED BY: Artur Jasinski
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Very strange, I tried the integral now on version 12.0, and the output is symbolic and correct:

1/4 (\[Pi]^2 Log[4] - 9 Zeta[3])
POSTED BY: Gianluca Gorni

I have access to 13,1
POSTED BY: Artur Jasinski
William Hedlin
William Hedlin
Posted 10 days ago

hope this helps? not really what you asked for, but related. I don't know... ignore bad or off variable names. I used gemini. no one prompt used, sources drawn from all over. I hold hallucination a possibility: either from gemini or mathematica bugs. that's my disclaimer, I guess.

POSTED BY: William Hedlin

With version 15 the integral does not give 0, it returns unevaluated. What looks to me like a bug is this result by IntegrateChangeVariables:

IntegrateChangeVariables[
 Inactive[Integrate][Sqrt[1 - x], {x, 0, 1}],
 y, y == Sqrt[1 - x]]
% // Activate

The output is zero, while it should be 2/3.
POSTED BY: Gianluca Gorni
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