Indeed. But no need for Mathematica :

sage: f(x)= sqrt(2+sqrt(2+sqrt(2+2*cos(5*sqrt(x)+4))))*x^(-1/2)
sage: h(x)= 2*cos(5/8*sqrt(x)+1/2)/sqrt(x)
sage: P1=plot(f(x),(x,0,120),ymin=-0.5, ymax=0.85)
sage: P2=plot(h(x),(x,0,120),ymin=-0.5, ymax=0.85)
sage: P1+P2

[image: tmp_a7yhgbnu.png]

BTW: How did you came to exhume a 4-years old thread ? 


Le samedi 24 août 2019 14:17:48 UTC+2, Rodrigo Sambade Saá a écrit :
>
> Dear William,
>
> Andrew is wrong 
> <https://www.wolframalpha.com/input/?i=2*cos%285%2F8*sqrt%28x%29%2B1%2F2%29%2Fsqrt%28x%29+%3D+sqrt%282%2Bsqrt%282%2Bsqrt%282%2B2*cos%285*sqrt%28x%29%2B4%29%29%29%29*x%5E%28-1%2F2%29>
> .
>
> Best wishes,
>
> Rodrigo 
>
> El jue., 12 feb. 2015 a las 21:57, William Stein (<wst...@gmail.com 
> <javascript:>>) escribió:
>
>> On Thu, Feb 12, 2015 at 12:55 PM, R. Andrew Ohana
>> <andre...@gmail.com <javascript:>> wrote:
>> > It is wrong, but not as wrong as you make it out to be. Your function 
>> is f =
>> > abs(h), where h = 2*cos(5/8*sqrt(x)+1/2)/sqrt(x). Rather that 
>> integrating f,
>> > it seems to have integrated h.
>>
>> Andrew -- very good point!  That's not nearly as bad as I made it out.
>>   Thanks,
>>
>>  -- William
>>
>> >
>> > --
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>>
>>
>> -- 
>> William (http://wstein.org)
>>
>

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