Date: Apr 26, 2013 3:47 PM
Author: Axel Vogt
Subject: integration test suite / Chap 3

These are the excercises for Chap 3 in Timofeev's book,
p.101 #1 - #3, p.105 #4 - #9, p.109 #10 - #12, p.113 #13, #14

Two of them are 'reductions formula' for a linear term, #4 and #5.
For those I have no idea how to test with Maple - they should be
done by partial integration and thus I ignore them.

The others seem to be for applying decomposition using partial
fractions. For which I suppose, that all CAS do it. There seem
to be no sophisticated cases there, so I just state _some_.

Maple 17 do them all (and I was to lazy to check for typos in
the results given in the book):

L:=[
#7
Int( (2*x-3) / (3+6*x +2*x^2)^3,x),
#9
Int(1/(x^2+3*x+2)^5,x),
#11
Int(x^9/(x^2+3*x+2)^5, x),
#12
Int((1+2*x)^2/(3+5*x+2*x^2)^5,x),
#13
Int( (a-b*x^2)^3/x^7,x),
#14
Int(x^13/(a^4+x^4)^5,x)
];

Now let the system evaluate, differentiate w.r.t. x and let
it check, whether the integrand is recovered:

map( t -> diff(value(t),x) = op(1,t), L);
simplify(%);
map(is, %);

[true, true, true, true, true, true]

Sorry for a non-complete treatment.