# integration ends up with hypergeometric function can not be done by sage

we know the integration of

1/(a^b+1)


with respect to a is going to get

2F1(1,1/a,1+1/a,-a^x)

where 2f1 is hypogeometric function. However, once we to that in sage, it is not possible to get results

sage: integrate(1/(x^b+1),x)
integrate(1/(x^b + 1), x)


hope this can be fixed up latter or have some alternative way to work around.

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Sort by » oldest newest most voted It seems sage's default algorithm can't do it. You can use mathematica's algorithm to do it in sage. You don't need mathematica installed on you computer. Just type the following command.

b=var('b')
integral(1/(x^b+1),x,algorithm='mathematica_free')

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Correct - see Trac 2516 for the current status.

See this Bessel function doc for an example that might help you by using Maxima more directly in your own context.

sage: m = maxima(bessel_J(2, x))
sage: m.integrate(x)
hypergeometric([3/2],[5/2,3],-x^2/4)*x^3/24


Also related - Trac 9908.

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Though apparently Maxima can't do this particular integral either.