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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