Question

Помогите, пожалуйста, решить интегралы!

Answer 1

Ответ:

5.1

$\int\limits(8 {x}^{3} - 3 {x}^{2} + 4x + 1)dx = \\ = \frac{8 {x}^{4} }{4} - \frac{3 {x}^{3} }{3} + \frac{4 {x}^{2} }{2} + x + C= \\ = 2 {x}^{4} - {x}^{3} + 2 {x}^{2} + C$

5.2

$\int\limits32 {(8x - 15)}^{3} dx = \int\limits4 \times 8 {(8x - 15)}^{3} dx = \\ = 4\int\limits {(8x - 15)}^{3} d(8x) = 4\int\limits {(8x - 15)}^{3} d(8x - 15)\\ = 4 \times \frac{ {(8x - 15)}^{4} }{4} +C = {(8x - 15)}^{4} + c$

5.3

$\int\limits^{ - 2} _ { - 5}(5 - 6x - {x}^{2})dx = (5x - \frac{6 {x}^{2} }{2} - \frac{ {x}^{3} }{3} ) | ^{ - 2} _ { - 5} = \\ = (5x - 3 {x}^{2} - \frac{ {x}^{3} }{3}) | ^{ - 2} _ { - 5} = \\ = - 10 - 12 + \frac{8}{3} - ( - 25 - 75 + \frac{125}{3} ) = \\ = - 22 + \frac{8}{3} + 100 - \frac{125}{3} = 78 - \frac{117}{3} = \\ = 78 - 39 = 39$