Вычислите интеграл 254.1) [ 3x² dx; 4) [4t3 dt; 256.1) [ 5x dx; 4) (3x - ex- 1) dx; 2)x4 dx; 5)dx x-2 2)42x dx; 5) 2dx x +3

1. \[\int 3x^2 dx = 3 \int x^2 dx = 3 \cdot \frac{x^3}{3} + C = x^3 + C\]

2. \[\int 4t^3 dt = 4 \int t^3 dt = 4 \cdot \frac{t^4}{4} + C = t^4 + C\]

3. \[\int 5^x dx = \frac{5^x}{ln(5)} + C\]

4. \[\int (3x - e^x - 1) dx = 3 \int x dx - \int e^x dx - \int 1 dx = 3 \cdot \frac{x^2}{2} - e^x - x + C = \frac{3}{2}x^2 - e^x - x + C\]

5. \[\int x^4 dx = \frac{x^5}{5} + C\]

6. \[\int \frac{dx}{x-2} = ln|x-2| + C\]

7. \[\int 4^{2x} dx = \int (4^2)^x dx = \int 16^x dx = \frac{16^x}{ln(16)} + C = \frac{16^x}{4ln(2)} + C\]

8. \[\int \frac{2}{x+3} dx = 2 \int \frac{1}{x+3} dx = 2 ln|x+3| + C\]

Ответ: Интегралы вычислены выше.