Expert: Abe Mantell - 7/11/2009

Question
I am struggling to integrate x^3 divided by (2-x)^3.

Any help would be appreciated.

Answer
Hello Rod,

Int(x^3/(2-x)^3 dx)...make a substitution: let u=2-x ==> x=2-u, dx=-du

Thus, we get: int((2-u)^3/u^3 * -du) = -int((2-u)^3/u^3 du)
Now expand (2-u)^3 to get 8-12u+6u^2-u^3.  So, the new integral
is -int((8-12u+6u^2-u^3)/u^3 du) = -int(8u^-3 - 12u^-2 + 6/u -1 du)

I think you can take it from here, yes?  Integrate each term, then
replace u with 2-x...OK?

Abe