Proble : maxima finds a primitive, but not a defnite integral.

>>>>> "Emmanuel" == Emmanuel Charpentier <emm.charpentier at free.fr> writes:

    Emmanuel> Dear list,
    Emmanuel> Could some kind soul explain to me why maxima

[snip]

    Emmanuel> can easly find this primitive :

    Emmanuel> (%i1) integrate(1/(1+sqrt(x)), x);
    Emmanuel> (%o1)                2 (sqrt(x) + 1) - 2 log(sqrt(x) + 1)

    Emmanuel> but does not appy it to this definite integral :

    Emmanuel> (%i2) integrate(1/(1+sqrt(x)), x, 0, 1);

[snip]

    Emmanuel> In other words, WTF ???

If you can, please file a bug report about this.  For this particular
integral, it turns out that poles-in-interval returns unknown, so
maxima gives up.  I guess that means solve couldn't find the zeroes of
1+sqrt(x).  If you set intanalysis:false, then the definite integral
is returned correctly.

    Emmanuel> PS : an, oh, by the way quad_qags

    Emmanuel> (%i5) quad_qags(1/(1+sqrt(x)), x, 0, 1);
    Emmanuel> (%o5)         [0.61370563888011, 2.5191337904573174E-10, 231, 0]

    Emmanuel> seems preferable to quad_qag

    Emmanuel> (%i6) quad_qag(1/(1+sqrt(x)), x, 0, 1, 6);
    Emmanuel> (%o6)          [0.6137056388632, 3.5930198130608816E-9, 1159, 0]

    Emmanuel> In this example. Again, why ?

Why do you think quad_qag should do better than quad_qags for this
integrand?

I'm not 100% sure, but I think quad_qags does better because it
handles the case of the infinite slope at zero better.  But I don't
have the quadpack book to understand which cases should perform
better.

Ray