 I thought I had done something amazing and beautiful — not solving the general integral, but massaging the section. ;-) For the record, Mathematica gives a closed-form antiderivative with a free in (0,1) as :::::::: ::::::: where 2F1 denotes a hypergeometric function. Imagine throwing that at the kiddies! ::::::: Actually, just for cultural orientation maybe the article should give an example somewhere of how a modest little integrand can produce a scary sprawling result. Calculus book examples are seriously misleading in lulling students into thinking most integrals have tidy little closed form results; tables of integrals are not much better.    