3.) б.) $$\int (2x^3 - x) dx = $$

Let's solve the integral: $$\int (2x^3 - x) dx$$ We can split the integral into two separate integrals: $$\int 2x^3 dx - \int x dx$$ Now, we integrate each term separately. Recall that $$\int x^n dx = \frac{x^{n+1}}{n+1} + C$$. $$\int 2x^3 dx = 2 \int x^3 dx = 2 \cdot \frac{x^{3+1}}{3+1} + C_1 = 2 \cdot \frac{x^4}{4} + C_1 = \frac{x^4}{2} + C_1$$ $$\int x dx = \frac{x^{1+1}}{1+1} + C_2 = \frac{x^2}{2} + C_2$$ Now we combine the results: $$\int (2x^3 - x) dx = \frac{x^4}{2} - \frac{x^2}{2} + C$$ where $$C = C_1 - C_2$$ Answer: $$\frac{x^4}{2} - \frac{x^2}{2} + C$$