# Math Help - integration question

1. ## integration question

i was wondering about an basic integration technique, the integral of (a+b)^y da and how this may be integrated insede the braket however if the thing inside the braket is not linear e.g.(a^x+b)^y da why it cannot be integrated inside the braket basically and i was wondering how to prove this??
thanks

2. 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.