Hi - maybe this is of interest -

" ...integral is non elementary by Chebyshev's theorem. In general,

the integral of x^p (a + b x^r)^q dx is elementary if and only if

at least one of (p+1)/r, q, or (p+1)/r + q is an integer

(see Marchisoto & Zakeri: "An Invitation to Integration in Finite

Terms", The College Mathematics Journal, Vol. 25, No. 4, Sept.1994,

pp.295-308).

Miguel A. Lerma

8/24/95 " at

http://www.math.niu.edu/~rusin/known...elementary.int

Or maybe you just need to notice that 'integrating inside the bracket' would mean following the chain rule for differentiation, and that's why you generally need the x^p in your integrand. But, as seem to notice (here, and before at http://www.mathhelpforum.com/math-he...technique.html) the p will be zero for r = 1.