∫(x³+4x)dx

Решение:

1. $$\int (x^3+4x) dx = \int x^3 dx + \int 4x dx$$
2. $$\int x^3 dx = \frac{x^{3+1}}{3+1} + C = \frac{x^4}{4} + C$$
3. $$\int 4x dx = 4 \int x dx = 4 \cdot \frac{x^{1+1}}{1+1} + C = 4 \cdot \frac{x^2}{2} + C = 2x^2 + C$$
4. $$\int (x^3+4x) dx = \frac{x^4}{4} + 2x^2 + C$$

Ответ: $$\frac{x^4}{4} + 2x^2 + C$$