Question

Решите пожалуйста!!! СРОЧНО

Answer 1

Ответ:

1

$\int\limits \frac{ {(2x - 1)}^{2} }{x} dx = \int\limits\frac{4 {x}^{2} - 4x + 1 }{x} dx = \\ = \int\limits(4x - 4 + \frac{1}{x}) dx = \frac{4 {x}^{2} }{2} - 4x + ln( |x| ) + C = \\ = 2 {x}^{2} - 4x + ln( |x| ) + C$

2.

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

3.

$\int\limits \frac{ {x}^{3} - 2 {x}^{2} - 3x - 4 }{ {x}^{2} } dx = \int\limits(x - 2 - \frac{3}{x} - \frac{4}{ {x}^{2} } )dx = \\ = \frac{ {x}^{2} }{2} - 2x - 3 ln( |x| ) - \frac{ 4 {x}^{ - 1} }{( - 1)} + c = \\ = \frac{ {x}^{2} }{2} - 2x - 3 ln( |x| ) + \frac{4}{x} + C$

4.

$\int\limits(4 \sin(x) - e {}^{x} - {3}^{x} + 8)dx = \\ = - 4 \cos(x) - {e}^{x} - \frac{ {3}^{x} }{ ln(3) } + 8x + C$