Another incorrect Maxima integral

[kcrisman]

This is already reported upstream at this bug tracker ticket.

The original report from a summer PREP user:

integral((2/3)*x^(5/2)*(x+1)^.5, x,0,1)

I got the answer -0.888888889*sqrt(2)

integral((2/3)*x^(5/2)*(x+1)^(1/2), x,0,1)

And the answer is


-5/192*I*pi + 61/288*sqrt(2) + 5/192*log(-sqrt(2) + 1) -
5/192*log(sqrt(2) + 1)

Upstream: Reported upstream. No feedback yet.

Component: calculus

Keywords: integral

Issue created by migration from https://trac.sagemath.org/ticket/13718

[kcrisman]

comment:1

#11493 may be related.

[mforets]

comment:6

This prompts me to see what happens with alternative integration interfaces.

Try with SymPy:

sage: sage: integral((2/3)*x^(5/2)*(x+1)^.5, x,0,1, algorithm='sympy')   
# no output at all after ~10mins

Try with giac:

sage: giac('integrate((2/3)*x^(5/2)*sqrt(x+1), x,0,1)')   # correct and almost instantaneous
1/288*(sqrt(2)*61+15*ln(sqrt(2)-1))
sage: (1/288*(sqrt(2)*61+15*ln(sqrt(2)-1))).n()
0.253633414928700
sage: (-5/192*I*pi + 61/288*sqrt(2) + 5/192*log(-sqrt(2) + 1) -
....: 5/192*log(sqrt(2) + 1)).n()    # compare with formula given by OP
0.253633414928700