4dx 5)/(12-6x)5 6) [ sin 4x dx. Вариант 5. 8dx 5) (7-5x); 6) [ cos 7x dx. Вариант 6. +1) dx; 4 +11x10 dx; 2) 3) [(5x²+10x - 1)dx; 4) [(8x - 2) dx; 4dx 5)(1-3x)5 3) [(6x5 + 4x - 2,5)dx; 4) [(3x - 2)7 dx; 5dx 5) (3-7x); 6) [ sin 2x dx. Вариант 7. 6) [ cos 6x dx. Вариант 8. 1) 2) 3) (6x11 + 4x - 1)dx; 4) [(7x - 3)³ dx; 5) 12dx 6) [ sin 3x dx. Вариант 9. 3 1 dx; +9x8 dx; 3) (5x2+3x-2)dx; +2x³ dx; 3) [(8x² + 3x - 15)dx; 4) (4x - 3) dx; 4dx 5)(3-6x); 6) [ cos 3x dx. Вариант 10. 2)3x- 2 +20x9 dx; 3) (4x³ + 7x - 2)dx;

Ответ: Решения представлены ниже

Вариант 5

1. \[\int (8 - x^{-4} + \frac{3}{x^6}) dx = 8x + \frac{1}{3x^3} - \frac{3}{5x^5} + C\]

2. \[\int (3x - \frac{4}{x^5} + 11x^{10}) dx = \frac{3}{2}x^2 + \frac{1}{x^4} + x^{11} + C\]

3. \[\int (5x^2 + 10x - 1) dx = \frac{5}{3}x^3 + 5x^2 - x + C\]

4. \[\int (8x - 2)^7 dx = \frac{1}{8} \cdot \frac{(8x - 2)^8}{8} + C = \frac{(8x - 2)^8}{64} + C\]

5. \[\int \frac{4dx}{(12 - 6x)^5} = \frac{4}{(-6)} \cdot \frac{(12 - 6x)^{-4}}{-4} + C = -\frac{2}{3} \cdot \frac{1}{-4(12 - 6x)^4} + C = \frac{1}{6(12 - 6x)^4} + C\]

6. \[\int sin(4x) dx = -\frac{1}{4}cos(4x) + C\]

Вариант 6

1. \[\int \sqrt[5]{(7 - 5x)^8} dx = \int (7 - 5x)^{\frac{8}{5}} dx = -\frac{1}{5} \cdot \frac{5}{13}(7 - 5x)^{\frac{13}{5}} + C = -\frac{1}{13}(7 - 5x)^{\frac{13}{5}} + C\]

2. \[\int cos(7x) dx = \frac{1}{7}sin(7x) + C\]

Вариант 7

1. \[\int (4 - x^7 + \frac{1}{x^7}) dx = 4x - \frac{x^8}{8} - \frac{1}{6x^6} + C\]

2. \[\int (9x - \frac{3}{x^4} + 2x^5) dx = \frac{9}{2}x^2 + \frac{1}{x^3} + \frac{1}{3}x^6 + C\]

3. \[\int (6x^{11} + 4x - 1) dx = \frac{1}{2}x^{12} + 2x^2 - x + C\]

4. \[\int (7x - 3)^3 dx = \frac{1}{7} \cdot \frac{(7x - 3)^4}{4} + C = \frac{(7x - 3)^4}{28} + C\]

5. \[\int 12 dx = 12x + C\]

6. \[\int sin(2x) dx = -\frac{1}{2}cos(2x) + C\]

Вариант 8

1. \[\int (5x^{\frac{14}{6}} + 22x^3) dx = \int (5x^{\frac{7}{3}} + 22x^3) dx = 5 \cdot \frac{3}{10}x^{\frac{10}{3}} + \frac{22}{4}x^4 + C = \frac{3}{2}x^{\frac{10}{3}} + \frac{11}{2}x^4 + C\]

2. \[\int (6 - x^{-8} + \frac{1}{x}) dx = 6x + \frac{1}{7x^7} + ln|x| + C\]

3. \[\int (8x^2 + 3x - 15) dx = \frac{8}{3}x^3 + \frac{3}{2}x^2 - 15x + C\]

4. \[\int (4x - 3)^7 dx = \frac{1}{4} \cdot \frac{(4x - 3)^8}{8} + C = \frac{(4x - 3)^8}{32} + C\]

5. \[\int \frac{4dx}{(3 - 6x)^6} = \frac{4}{(-6)} \cdot \frac{(3 - 6x)^{-5}}{-5} + C = -\frac{2}{3} \cdot \frac{1}{-5(3 - 6x)^5} + C = \frac{2}{15(3 - 6x)^5} + C\]

6. \[\int cos(6x) dx = \frac{1}{6}sin(6x) + C\]

Вариант 9

1. \[\int (10 - x^{-6} + \frac{1}{x^6}) dx = 10x + \frac{1}{5x^5} - \frac{1}{5x^5} + C\]

2. \[\int (\frac{6x}{x^9} + 9x^8) dx = \int (6x^{-8} + 9x^8) dx = -\frac{6}{7x^7} + x^9 + C\]

3. \[\int (5x^2 + 3x - 2) dx = \frac{5}{3}x^3 + \frac{3}{2}x^2 - 2x + C\]

4. \[\int (\frac{6x^2}{x^4} + 2x^3) dx = \int (6x^{-2} + 2x^3) dx = -\frac{6}{x} + \frac{1}{2}x^4 + C\]

5. \[\int \frac{4dx}{(3 - 6x)^6} = \frac{4}{(-6)} \cdot \frac{(3 - 6x)^{-5}}{-5} + C = -\frac{2}{3} \cdot \frac{1}{-5(3 - 6x)^5} + C = \frac{2}{15(3 - 6x)^5} + C\]

6. \[\int sin(3x) dx = -\frac{1}{3}cos(3x) + C\]

Вариант 10

1. \[\int (5 - 2x^5 + \frac{1}{x^9}) dx = 5x - \frac{1}{3}x^6 - \frac{1}{8x^8} + C\]

2. \[\int (3x - \frac{2}{x^8} + 20x^9) dx = \frac{3}{2}x^2 + \frac{2}{7x^7} + 2x^{10} + C\]

3. \[\int (4x^3 + 7x - 2) dx = x^4 + \frac{7}{2}x^2 - 2x + C\]

4. \[\int \frac{4dx}{(4x - 3)^7} = \frac{4}{4} \cdot \frac{(4x - 3)^{-6}}{-6} + C = -\frac{1}{6(4x - 3)^6} + C\]

5. \[\int \frac{4dx}{(3 - 6x)^6} = \frac{4}{(-6)} \cdot \frac{(3 - 6x)^{-5}}{-5} + C = -\frac{2}{3} \cdot \frac{1}{-5(3 - 6x)^5} + C = \frac{2}{15(3 - 6x)^5} + C\]

6. \[\int cos(3x) dx = \frac{1}{3}sin(3x) + C\]

Ответ: Решения представлены ниже