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# Is there a way to integrate sqrt(x+sqrt(x)) in Sage?

Anonymous

Hello, I want to get indefiniteIntegral of sqrt(x+sqrt(x)), But in Sage, I get nothing but integrate(sqrt(x + sqrt(x)), x).

sage: x = var('x')
sage: h = sqrt(x+sqrt(x))
sage: h.integral(x)


Is there a way to integrate this function?

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## 1 Answer

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With optional package fricas (installable with sage -i fricas), it does something:

sage: integrate(sqrt(x + sqrt(x)), x, algorithm='fricas')
1/12*(8*x + 2*sqrt(x) - 3)*sqrt(x + sqrt(x)) + 1/16*log(4*sqrt(x + sqrt(x))*(2*sqrt(x) + 1) + 8*x + 8*sqrt(x) + 1)


But indeed, maxima, sympy and giac have trouble with it:

sage: integrate(sqrt(x + sqrt(x)), x, algorithm='maxima')
integrate(sqrt(x + sqrt(x)), x)
sage: integrate(sqrt(x + sqrt(x)), x, algorithm='sympy')
integrate(sqrt(x + sqrt(x)), x)
sage: integrate(sqrt(x + sqrt(x)), x, algorithm='giac')
...
TypeError: An error occurred running a Giac command:  ...

more

## Comments

Thank you for helping me!

( 2020-04-21 10:10:33 +0200 )edit

The problem with giac might be related to https://trac.sagemath.org/ticket/28913

( 2020-04-21 14:14:26 +0200 )edit

It was not related to #28913, I created https://trac.sagemath.org/ticket/29966

( 2020-06-24 22:17:09 +0200 )edit

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Asked: 2020-04-21 06:31:32 +0200

Seen: 386 times

Last updated: Apr 21 '20