Integration of x**(S(9)/2) * log(x) takes about 15 minutes

[normalhuman]

The integration of x**(S(9)/2) * log(x) is an easy calculus exercise (by parts once), but SymPy takes about 15 minutes on my computer.

>>> from sympy import *
>>> from time import time
>>> x = symbols('x', positive=True)
>>> tc = time(); integrate(x**(S(9)/2)*log(x), x); print(time() - tc)
2*x**(11/2)*log(x)/11 - 4*x**(11/2)/121
947.0029301643372

The amount of time grows rapidly with the exponent; I would not want to try 99/2.

Should manual integration be tried before heurisch (which takes so long)?

>>> tc = time(); integrate(x**(S(9)/2)*log(x), x, manual=True); print(time() - tc)
4*x**(11/2)*log(x**(9/2))/99 - 4*x**(11/2)/121
0.660252571105957

[jksuom]

Should manual integration be tried before heurisch

That is how it was planned, originally. I guess that the ordering of integrators became hard to implement as _eval_integral is calling itself recursively.

[asmeurer]

heurisch should absolutely be called very last.

[RituRajSingh878]

I think there is an issue in "manualintegrate" because it is giving the wrong result for the above integrand when the manual is "True".

[RituRajSingh878]

@asmeurer after changing order of integrators ,many test case are failing .so i think we can add time limit function in heurisch so it will break it's self after some time and continue to other integrators.

[sharma-kunal]

@asmeurer I would like to work on the issue, if you tell me how we can make heurisch to be called at last.

[sharma-kunal]

or we can do as proposed by @RituRajSingh878