The given integral is:

$\int (3x^2 - 2x) \, dx$

To solve this, integrate each term separately:

1. The integral of $3x^2$ is: $\int 3x^2 \, dx = x^3$

2. The integral of $-2x$ is: $\int -2x \, dx = -x^2$

Now, combining these results:

$\int (3x^2 - 2x) \, dx = x^3 - x^2 + C$

Where $C$ is the constant of integration.

Would you like more details on this process, or do you have any questions?

Related Questions:

1. How do you handle integrals with more complex polynomials?
2. What are the rules for integrating trigonometric functions?
3. Can you explain how definite integrals work?
4. How do you apply the power rule in integration?
5. What is the difference between indefinite and definite integrals?

Tip:

When integrating polynomials, remember to apply the power rule: $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$ for $n \neq -1$.