Question

помогите пожалуйста!!!!!!​

Answer 1

Ответ:

1

$\int\limits(25 {x}^{4} - 16x + 7)dx = ( \frac{ {25x}^{5} }{5} - \frac{16 {x}^{2} }{2} + 7x + C= \\ = 5 {x}^{5} - 8 {x}^{2} + 7x + C$

2

$\int\limits(4x - 3)(5 + x)dx = \int\limits(20x + 4 {x}^{2} - 15 - 3x)dx = \\ = \int\limits(4 {x}^{2} + 17x - 15)dx = \frac{4 {x}^{3} }{3} + \frac{17 {x}^{2} }{2} - 15x + C$

3

$\int\limits(2 - x - {x}^{2} ) {x}^{2}dx = \int\limits(2 {x}^{2} - {x}^{3} - {x}^{4} )dx = \\ = \frac{2 {x}^{3} }{3} - \frac{ {x}^{4} }{4} - \frac{ {x}^{5} }{5} + C$

4

$\int\limits( \frac{x - 8 {x}^{3} }{ {x}^{2} } )dx = \int\limits( \frac{x}{ {x}^{2} } - \frac{8 {x}^{3} }{ {x}^{2} } )dx = \\ = \int\limits( \frac{1}{x} - 8)dx = ln |x| - 8x + C$

5

$\int\limits( \sqrt{ {x}^{3} } - \frac{5}{ \sqrt{ {x}^{3} } } )dx = \int\limits( {x}^{ \frac{3}{2} } - 5 {x}^{ - \frac{3}{2} } )dx = \\ = \frac{ {x}^{ \frac{5}{2} } }{ \frac{5}{2} } - \frac{5 {x}^{ - \frac{1}{2} } }{ - \frac{1}{2} } + C = \frac{2}{5} {x}^{2} \sqrt{x} + \frac{10}{ \sqrt{x} } + C$

6

$\int\limits(13 \sin(x) + 15 \cos(x))dx = - 13 \cos(x) + 15 \sin(x) + C$

7

$\int\limits( {9}^{x} + 9 {e}^{x} )dx = \frac{ {9}^{x} }{ ln(9) } + 9 {e}^{x} + C$

8

$\int\limits(10 + \cos(x)) dx = 10x + \sin(x) + C$

9

$\int\limits( \frac{2 \sin {}^{2} (x) - 4 }{ 8\sin {}^{2} (x) } )dx = \int\limits( \frac{2 \sin {}^{2} (x) }{ 8\sin {}^{2} (x) } - \frac{4}{8 \sin {}^{2} (x) } )dx = \\ = \int\limits( \frac{1}{4} - \frac{1}{2 \sin {}^{2} (x) } )dx = \frac{1}{4} x + \frac{1}{2} ctg(x) + C$

10

$\int\limits(12 {x}^{3} - 5 {x}^{2} + 11 {e}^{x} )dx = \frac{12 {x}^{4} }{4} - \frac{5 {x}^{3} }{3} + 11 {e}^{x} + c = \\ = 3 {x}^{4} - \frac{5 {x}^{3} }{3} + 11 {e}^{x} + C$

11

$\int\limits(7 {x}^{ - 3} + 8 {x}^{ - 2} - \frac{9}{x} - \frac{10}{ \cos {}^{2} (x) } )dx = \\ = \frac{7 {x}^{ - 2} }{ - 2} + \frac{8 {x}^{ - 1} }{ - 1} - 9ln |x| - 10tg(x) +C = \\ = - \frac{7}{2 {x}^{2} } - \frac{8}{x} - 9ln |x| - 10tg(x) + C$

12

$\int\limits( {x}^{9} + {9}^{x} )dx = \frac{ {x}^{10} }{10} + \frac{ {9}^{x} }{ ln(9) } + C$

13

$\int\limits(18 + 15 {x}^{ - 2} - \frac{3}{4} {x}^{ - \frac{1}{2} } )dx = \\ = 18x + \frac{15 {x}^{ - 1} }{ - 1} - \frac{3 {x}^{ \frac{1}{2} } }{4 \times \frac{1}{2} } + C = \\ = 18x - \frac{15}{x} - \frac{3}{2} \sqrt{x} + C$

14

$\int\limits(9 {x}^{3} - 8 {x}^{2} + 7)dx = \frac{9 {x}^{4} }{4} - \frac{8 {x}^{3} }{3} + 7x + C$

15

$\int\limits(x - 2)(5x + 3)dx = \int\limits(5 {x}^{2} + 3x - 10x - 6)dx = \\ = \int\limits(5 {x}^{2} - 7x - 6)dx = \frac{5 {x}^{3} }{3} - \frac{7 {x}^{2} }{2} - 6x + C$