  Author presents a study of certain category of the integrals, which might
look quite difficult to compute, but in fact are easily computable, because
they do not depend on the parameter in the integrand. As simple and elementary
the procedure is, the author discovered that the best of symbolic manipulation
packages presently available fail quite miserably, when asked to compute these
integrals. The author suggests proper modifications in the algorithms used for
symbolic integration.
