I thought I had done something amazing and beautiful  not solving the general integral but massaging the section  For the record Mathematica gives a closedform antiderivative with a free in  as   where F 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