I think it is correct, at least algebraically:
In [6]: a = S("-1/12*(3*(sqrt(x) + 1)^(5/2)/x^(5/4) - 8*(sqrt(x) +
1)^(3/2)/x^(3/4) - 3*sqrt(sqrt(x) + 1)/x^(1/4))/((sqrt(x) + 1)^3/x^(3/2) -
3*(sqrt(x) + 1)^2/x + 3*(sqrt(x) + 1)/sqrt(x) - 1) + 1/8*log(sqrt(sqrt(x) +
1)/x^(1/4) + 1) - 1/8*log(sqrt(sqrt(x) + 1)/x^(1/4) - 1)")
In [7]: print(simplify(a.diff(x)))
x**(1/4)*sqrt(sqrt(x) + 1)
(if you distribute sqrt(sqrt(x)) inside the sqrt(sqrt(x) + 1) you get
sqrt(x + sqrt(x))
Aaron Meurer
On Thu, Jul 23, 2015 at 2:37 PM, Kalevi Suominen <[email protected]> wrote:
>
>
> On Thursday, July 23, 2015 at 8:31:41 PM UTC+3, Denis Akhiyarov wrote:
>>
>> Sympy cannot do this?
>>
>> integrate(sqrt(x+sqrt(x)))
>>
>> BTW, this is computed by SAGE:
>>
>> -1/12*(3*(sqrt(x) + 1)^(5/2)/x^(5/4) - 8*(sqrt(x) + 1)^(3/2)/x^(3/4) -
>> 3*sqrt(sqrt(x) + 1)/x^(1/4))/((sqrt(x) + 1)^3/x^(3/2) - 3*(sqrt(x) + 1)^2/x
>> + 3*(sqrt(x) + 1)/sqrt(x) - 1) + 1/8*log(sqrt(sqrt(x) + 1)/x^(1/4) + 1) -
>> 1/8*log(sqrt(sqrt(x) + 1)/x^(1/4) - 1)
>>
>
>
> I Is it possible to verify that this really is a solution. The integrand
> seems to belong to an elliptic function field where integration rarely
> succeeds in terms of algebraic expressions.
>
>
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