[Maxima-discuss] Unexpected result from Trig-sub integral

[Rex A. <Rex...@tc...>]

I am using Lon-Capa, which uses Maxima as a math brain) with my Calculus 2 class.  I have a homework problem that none of my students could get correct, so I investigated and discovered this phenomenon.

Maxima 5.40.0 http://maxima.sourceforge.net
using Lisp CLISP 2.49 (2010-07-07)
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) logarc:false;
(%o1)                                false
(%i2) assume(x>3);
(%o2)                               [x > 3]
(%i3) integrate(sqrt(x^2-9)/x,x);
                                2                     3
(%o3)           sqrt(x  - 9) + 3 asin(-)
                                                       x
(%i4)

When I do this integral by hand, instead of asin(x/3), I expect asin(sqrt(x^2-9)/x) (or acos(x/3) or atan(sqrt(x^2-9)/x) ).

The substitution x = 3 sec(theta) is used to perform the integral, and I discourage my students from using the inverse secant, inverse cosecant, and inverse cotangent functions in their results.  Maxima seems to prefer that stance as well.

Is there some subtlety to this that I am missing?

Rex Abert


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