Method of integrating (x^2 - 6)^4?

Question

Method of integrating (x^2 - 6)^4?

Answer 1

Well naturally you'd like to do it without multiplying out the brackets, however this isn't possible since there is an x^2 term in the brackets.

So then you might want to look for a substitution, but this doesn't work because the power is 4 in the brackets.

so unfortunately they only way to work this out is to use the binomial expansion (http://en.wikipedia.org/wiki/Binomial_ex... to multiply out the brackets and then integrate each term normally.

Quite annoying. After integrating, the answer is (x^9)/9 -(24x^7)/7 + (216x^5)/5 - 288x^3 + 1296x. But I'll spare you the working :)