**Integral of (x^3-2x^3)/(x^2(x-2))**

To find the integral of the given expression, we can start by simplifying it.

**Simplifying the expression**

The given expression is (x^3-2x^3)/(x^2(x-2)).

To simplify it, let's factor out x^3 from the numerator:
x^3(1-2)/(x^2(x-2))

Simplifying further:
-x^3/x^2(x-2)

Now, we can cancel out x^3 and x^2 from the numerator and denominator, respectively:
-1/(x-2)

**Finding the integral**

The integral of -1/(x-2) can be found using the substitution method.

Let's substitute u = x-2, which means du = dx.

Now, we can rewrite the integral as:
∫ -1/du

Simplifying further:
-∫ du

The integral of du is simply u:
- u + C

**Substituting back**

We initially substituted u = x-2, so we need to substitute it back to get the final answer.

Therefore, the integral of (x^3-2x^3)/(x^2(x-2)) is:
- (x-2) + C

where C is the constant of integration.

**Final Answer**

The final answer is:
∫ (x^3-2x^3)/(x^2(x-2)) dx = - (x-2) + C