Question

find the antiderivative of f(x) = x^3(x-2)^2

Someone help me please!

Answer 1

rather than resorting to some formula method, I would expand the whole thing, and then integrate each of the simple terms.

Answer 2

Would I square (x-2) first and then multiply it by x cubed, or x cubed multiplied by (x-2) and then square the answer? Order of operations is parenthesis, exponents, multiplication and division (left to right), and then addition and subtraction ( left to right), isn't it?

Answer 3

you would square x-2 first, the squaring does not include the x^3, or else the whole thing would have been in brackets, should have had...
x^3(x^2 - 4x+4)
= x^5 - 4x^4 + 4x^2

now integrate that

Answer 4

Integrate? Meaning?