
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 30second 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#x650005> >
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 nonelementary antiderivatives 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 ISqrt[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

