HP -32S Owner's Manual page 282

You can see that this function is 'interesting* only at small values of x.
At greater values of x, the function is not interesting, since it decreases
smoothly and gradually in a predictable manner.
The algorithm samples the function with higher densities of sample
points until the disparity between successive approximations becomes
sufficiently small. For a narrow interval in an area where the function
is interesting, it takes less time to reach this critical density.
To achieve the same density of sample points, the total number of
sample points required over the larger interval is much greater than
the number required over the smaller interval. Consequently, several
more iterations are required over the larger interval to achieve an ap
proximation with the same accuracy, and therefore calculating the
integral requires considerably more time.
Because the calculation time depends on how soon a certain density
of sample points is achieved in the region where the function is inter
esting, the calculation of the integral of any function will be
prolonged if the interval ofintegration includes mostiy regions where
the function is not interesting. Fortunately, if you must calculate such
an integral, you can modify the problem so that the calculation time is
considerably reduced. Two such techniques are subdividing the inter
val of integration and transformation of variables. These methods
enable you to change the function or the limits of integration so that
the integrand is better behaved over the interval(s) of integration.
280 D: More About Integration