The indefinite intergral of (x-1/3x)^2 dx equals

Question

anonymous · Answer

$$\int\limits_{?}^{?}(x-1/3x)^2 dx$$

amistre64 · Answer

if 3x is a demoniator; you might wanna start out by making the innards into a single term

amistre64 · Answer

3x^2 -1
--------  ; and square it
     3x

9x^4 -6x^2 +1
-------------- ; split it apart
       9x^2


9x^4        6x^2          1
-----  (-) ----- (+) ----- ; now simplfy and integrate perhpas?
9x^2         9x^2       9x^2

anonymous · Answer

I got 1/3x^3-2/3x-1/(9x)

But the choice given are:
a. 1/3(x-1/(3x))^2
b.x^2-2/3+1/(9x^2)
c.x^3/3-2x-1/(9x)
d. x^3/2-2/3 x-9/x
e.none of these

can u help me double check?

amistre64 · Answer

that is correct:

$$\frac{1}{3}x^3-\frac{2}{3}x-\frac{1}{9x} +C$$
$$\frac{3x^4-6x^2+C}{9x}$$
unless there is some algebra that I cant see, the answer would appear to be e"none of the above".

anonymous · Answer

Okay thanks alot!!