1 | initial version |

[ Not really an answer, but a complement to Serge's answer, in order too pinpoint the answer ]

A quick check:

```
f(x)=log(sqrt(x)+1)/sqrt(x)
def tst1(alg="maxima"):
ad=f(x).integrate(x, algorithm=alg)
check_ad=bool(ad.diff(x)==f(x))
ub=ad.limit(x=4)
lb=ad.limit(x=1)
di=(ub-lb).simplify()
did=f(x).integrate(x,1,4, algorithm=alg)
check_di=bool(di==did)
ndi=di.n()
# return [ad, check_ad, lb, ub, di, did, check_di, ndi]
return [alg, check_ad, di, did, check_di]
T=table(rows=[tst1(alg=u) for u in ["maxima", "sympy", "giac", "fricas"]],
header_row=["Algorithm", " AD checks", "Def. int. through AD",
"Def. int. directly", "Def. int. checks"])
```

shows that the antiderivative (aka primitive, AD) is correct (i.e. derivates back to f(x)) in all cases (and that its limits are correctly evaluated at each bound), but that the direct computation of the definite integral is wrong in Maxima :

```
Algorithm AD checks Def. int. through AD Def. int. directly Def. int. checks
+-----------+------------+-------------------------+---------------------------+------------------+
maxima True 6*log(3) - 4*log(2) - 2 4*log(3) + 2*log(4/3) - 2 False
sympy True 6*log(3) - 4*log(2) - 2 6*log(3) - 4*log(2) - 2 True
giac True 6*log(3) - 4*log(2) - 2 6*log(3) - 4*log(2) - 2 True
fricas True 6*log(3) - 4*log(2) - 2 6*log(3) - 4*log(2) - 2 True
```

This problem has been encountered more than once, is known to upstream, but does not seem to have been formally reported *per se*.

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