The following integrals, most of which appear in Integrals and Series [11], [12], [13] were calculated with the aid of the theorems and algorithm described in this paper.  The performance of two different computer algebra systems on this test suite is as follows: Maple 5.4 was able to compute a formula for one integral and left all the other integrals unevaluated.  Mathematica 2.2 left six integrals unevaluated, produced four answers which still contained hypergeometric functions , and only computed formulas for three of these integrals. 

(2.5.6(3) p390 v1)

(2.5.21(3b) p430 v1)

(2.7.6(6) p560 v1)

(2.12.19(6) p200 v2)

(2.12.31(1l) p210 v2)

(2.12.43(3) p233 v2)

(2.14.1(6a) p290 v2)

(2.15.20(4c) p320 v2)

(2.15.20(5f) p320 v2)

(2.16.15(1a) p360 v2)

(2.16.15(2a) p360 v2)

(2.7.16(3) p90 v3)