posted by on .

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

I factored this out and got
x^5-4x^4+4x^2

I'm supposed to integrate this. I don't know how. Someone help me please?

BTW, multiple choice options are:
A
B
C
D

Sorry, let me fix that. Multiple Choice options are:

A: 1/6 x^6 - 4/5 X^5 + x^4 + C
B: 1/6 x^6 - 4/5 X^5 + 1/4 x^4 + C
C: x^6 - X^5 + x^4 + C
D: x^5 - 4x^4 + 4x^3 + C

I assume this is a continuation of
http://www.jiskha.com/display.cgi?id=1335468769

That is the more "mathematical" terminology.
To "integrate" something is the same as finding the "anti-derivative"

e.g.
the derivative of 6x^3 + 5x - 2 is 18x^2 + 5
and the integral or the anti-derivative of 18x^2 + 5 is 6x^3 + 5x

btw, I had a typo in my expanded form, should have been
x^5 - 4x^4 + 4x^3 , I am surprised you didn't check that

so the anti-derivative or the integral of
x^5 - 4x^2 + 4x^3 is

(1/6)x^6 - (4/5)x^5 + x^4 + C , where C is a constant

clearly choice a)

(differentiate choice a) and see what you get, to verify the answer)