Homework Statement
In= (the integral) x(1-x^3)^ndx
Prove that (3n +2)In = 3nIn-1 + x^2(1 - x)^n
Hence find In in terms of n
The Attempt at a Solution
I tried integration by parts (by letting u be (1-x^3)^n and got stuck after this:
In = 1/2x^2(1-x^3)^n + (the...