Indefinite integral is known and not weird, but definite integral won't go

Dear list,

Title sums it up, and see below for exact issue.  It seems odd that
Maxima knows the indefinite integral, that said antiderivative doesn't
have a domain issue near the endpoints (and looks like a pretty
routine u-substitution), but the definite integral doesn't use the
FTC.   [Maple, Sympy, and Mathematica both do and say =1/2.]

At the same time, maybe there is some branch issue or something going
on here?  As usual, hesitant to cry "bug" where multivalued functions
are involved... so I'd be grateful for advice.

Thanks for any help, I'll file a bug report if need be!

(Originally from a sage-support thread.)


Maxima 5.25.0 http://maxima.sourceforge.net
using Lisp SBCL 1.0.24
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) integrate(1/(sqrt(x)*((1+sqrt(x))^2)),x,1,1);
(%o1)                                  0
(%i2) integrate(1/(sqrt(x)*((1+sqrt(x))^2)),x,1,9);
                          9
                         /
                         [            1
(%o2)                    I  ---------------------- dx
                         ]               2
                         /  (sqrt(x) + 1)  sqrt(x)
                          1
(%i3) integrate(1/(sqrt(x)*((1+sqrt(x))^2)),x);
                                        2
(%o3)                            - -----------
                                   sqrt(x) + 1