AboutAbe Mantell Expertise Hello,
I am a college professor of mathematics and regularly teach all levels
from elementary mathematics through differential equations, and would
be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
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?
