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Maple V includes a new method for computing definite integrals
based on evaluating the derivatives of special functions. For example,
it can compute integrals of the form
where 
,
and other restrictions on the constants apply.
In general these integrals can be expressed in terms of
the incomplete Gamma function, the Riemann zeta function,
the Meijer G function, and other special functions e.g.
> int( exp(-t)*cos(t)*ln(t), t=0..infinity );
where 
is Eulers constant.
The calculation below illustrates a new family of definite integrals
that Release 2 knows about and also the ability to make assumptions
about symbolic parameters. The answer to the integral below depends on
the parameters 
and 
, in this case whether they are positive or
negative. With no additional information, Maple cannot solve the problem.
The assume facility in Release 2 allows users to state assumptions about
symbolic parameters e.g. here that and are real and positive
> f := x^(a-1)*exp(-p*x^s-q*x^(-s));
> assume(p>0); assume(q>0);
> Int(f,x=0..infinity) = int(f,x=0..infinity);
