26: The derivative
is not simple enough to be handled easily. The standard procedure (finding
its crucial points, that is, zero points od the next, the fourth derivative)
leads to an equation of degree 3 that takes time to solve, so it is much
easier (though we will loose a bit) to first make the estimate a bit more
generous by taking maximum over the whole interval
Now we use it in estimating the error of integration.
Note that this is not so bad if we use it for small x. For instance,
for