
integration test suite / Chap 3
Posted:
Apr 26, 2013 3:47 PM


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*x3) / (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( (ab*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 noncomplete treatment.

