Question

Решить интегралы 30 баллов

Answer 1

Ответ:

1

$\int\limits2dx = 2x + C$

2

$\int\limits {x}^{5} dx = \frac{ {x}^{6} }{6} + C$

3

$\int\limits \frac{dx}{x} = ln( |x| ) + C$

4

$\int\limits \sin(x) dx = - \cos(x) + C$

5

$\int\limits6 {e}^{x}dx = 6e {}^{x} + C$

6

$\int\limits4 \cos(x) dx = 4\sin(x) + C$

7

$\int\limits(6x - 10) {}^{8} dx = \frac{1}{6}\int\limits {(6x - 10)}^{8} d(6x - 10) = \\ = \frac{ {(6x - 10)}^{9} }{54} + C$

8

$\int\limits(6 {x}^{3} + 8 {x}^{7} - 3 {x}^{8} )dx = \frac{6 {x}^{4} }{4} + \frac{ {8x}^{8} }{8} - \frac{3 {x}^{9} }{9} + C = \\ = 1.5 {x}^{4} + {x}^{8} - \frac{ {x}^{9} }{3} + C$

9

$\int\limits \sin(9x - \frac{ \pi}{5} ) dx = \frac{1}{9} \int\limits \sin(9x - \frac{\pi}{5} ) dx = \\ = - \frac{1}{9} \cos(9x - \frac{\pi}{5} ) + C$

10

$\int\limits(8 \cos(4x) - 2 \sqrt{x} + {e}^{5x + 2} )dx = \\ = 2\int\limits \cos(4x) d(4x) - 2 \times \frac{ {x}^{ \frac{3}{2} } }{ \frac{3}{2} } + \frac{1}{5} \int\limits {e}^{5x + 2} + C = \\ = 2 \sin(4x) - \frac{4}{3}x \sqrt{x} + \frac{ {e}^{5x + 2} }{5} + C$