Question

ДАЮ 35 БАЛЛОВ НАЙДИТЕ ИНТЕГРАЛ!!!

Answer 1

Ответ:

2.

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

5.

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

6.

$(2) = 0$

7.

$\int\limits \: xdx = \frac{ {x}^{2} }{2} + c$

8.

$\int\limits {e}^{x} dx = {e}^{x} + c$

9.

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

10.

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

11.

$(tgx) = \frac{1}{ { \cos}^{2}(x) }$

13.

$( - ctgx) = \frac{1}{ { \sin}^{2} x}$

14.

$\int\limits \: xdx = \frac{ {x}^{2} }{2} + c$

15.

$\int\limits(5 {e}^{x} + 7 \sin(x) - 3 {x}^{2} )dx = \\ = 5 {e}^{x} - 7 \cos(x) - {x}^{3} + c$

16.

$\int\limits {(2x - 3)}^{5} dx = \frac{1}{2} \int\limits {(2x - 3)}^{5} d(2x - 3) = \\ = \frac{1}{2} \times \frac{ {(2x - 3)}^{6} }{6} + c = \frac{ {(2x - 3)}^{6} }{12} + c$

17.

$\int\limits {(4 - 5x)}^{7} dx = - \frac{1}{5} \int\limits {(4 - 5x)}^{7} d(4 - 5x) = \\ = - \frac{1}{5} \times \frac{ {(4 - 5x)}^{8} }{8} + c = - \frac{ {(4 - 5x)}^{8} }{40} + c$

18.

$\int\limits5 \cos(3x) dx = \frac{1}{3} \int\limits \cos(3x) d(3x) = \\ = \frac{1}{3} \sin(3x) + c$

19.

$(6ctg(2x)) = - \frac{6}{ { \sin }^{2}(2x) } \times 2 = \\ = - \frac{12}{ { \sin }^{2} (2x)}$

20.

$( ln(x + 3)) = \frac{1}{x + 3}$

21.

$( - 3tg( - x)) = - 3 \times \frac{1}{ { \cos }^{2} (x)} \times ( - 1) = \\ = \frac{3}{ { \cos }^{2}(x) }$

22.

23.

$\int\limits3 \cos(3x + 2) dx = 3 \times \frac{1}{3} \int\limits \cos(3x + 2) d(3x + 2) = \\ = \sin( 3x + 2 ) + c$