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Topic: Charlwood Fifty test results
Replies: 16   Last Post: Sep 19, 2013 10:09 PM

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 Nasser Abbasi Posts: 6,677 Registered: 2/7/05
Re: Charlwood Fifty test results
Posted: Jul 6, 2013 10:26 PM

> So, while there is no real discrepancy between the Mathematica results
> for problems 7 and 9, your 30-second timeouts explain the (apparent)
> failures on problems 6 and 8. What remains to be explained are the
> incompatible Mathematica results for problem 5 where Nasser obtained an
> unevaluated integral:
>
> <http://www.12000.org/my_notes/ten_hard_integrals/inse5.htm#x6-50005>
>

This is really, really strange. I can't explain what happened.

I just run #5 now again on fresh kernel, with M 9.01 and now it gives
a result !

I really do not know why and how this has happened. You saw the output
and that it did not evaluate before.

This means M has 10/10 score now (but I do not do penalties for
non-elementary anti-derivatives and for long computation time, so
Albert's more advanced scoring scheme will give different rankings)

--------------------------------------------------------------
In[41]:= Integrate[Cos[x]^2/Sqrt[Cos[x]^4+Cos[x]^2+1],x]

Out[41]= -(2 I Cos[x]^2 EllipticPi[3/2+(I Sqrt[3])/2,I
ArcSinh[Sqrt[-((2 I)/(-3 I+Sqrt[3]))] Tan[x]],(3 I-Sqrt[3])/
(3 I+Sqrt[3])] Sqrt[1-(2 I Tan[x]^2)/(-3 I+Sqrt[3])]
Sqrt[1+(2 I Tan[x]^2)/(3 I+Sqrt[3])])/(Sqrt[-(I/(-3 I+Sqrt[3]))]
Sqrt[15+8 Cos[2 x]+Cos[4 x]])
-------------------------------------------------------------

Just updated page:

http://www.12000.org/my_notes/ten_hard_integrals/index.htm

Sorry again for this. I wish I know why it did not evaluate before
and thanks for spotting this.

--Nasser