1. Macsyma gets these examples right.
A relevant paper may be this one:
Evaluation of Classes of Definite Integrals Involving
Elementary Functions via Differentiation
of Special Functions
K. O. Geddes , M. L. Glasser , R. A. Moore and T. C. Scott .
AAECC Applicable Algebra in
Engineering, Communication
and Computing
? Springer-Verlag 1990