meijerint picks wrong branch for computing indefinite integrals of algebraic functions

[sylee957]

from sympy import *

f = x**-3 * (1 + x**4)**-Rational(1, 2)
F = integrate(f, x, meijerg=True)
print(F)

gives the result -sqrt(1 + x**(-4))/2 which does not equal to the integrand when differentiated

print(F.diff(x).xreplace({x: I}))
print(f.xreplace({x: I}))

-sqrt(2)*I/2
sqrt(2)*I/2

[Nbede]

Do you mean diff of integral should work even with complex numbers?
There's no issue with real numbers. After diff, it took out x^4 from inside the sqrt as x^2. for the complex number "I," hence there are two different answers as sqrt(i^4) is 1 and i^2 is -1.

[sylee957]

It should be because there is a correct closed-form solution that works for all the complex numbers.
-sqrt(1 + x**4)/2/x**2