Question

хоть 6-7 примеров
первообразная ​

Answer 1

15.

$f(x) = \int\limits(2 {x}^{6} - 2 {x}^{ - 5} - e)dx = \\ = \frac{2 {x}^{7} }{7} - \frac{2 {x}^{ - 4} }{( - 4)} - ex + C = \\ = \frac{2 {x}^{7} }{7} + \frac{1}{2 {x}^{4} } - ex + C$

16.

$f(x) = \int\limits(0.2 {x}^{5} - {x}^{3} - 7) dx = \\ = \frac{1}{5} \times \frac{ {x}^{6} }{6} - \frac{ {x}^{4} }{4} - 7x + C = \\ = \frac{ {x}^{6} }{30} - \frac{ {x}^{4} }{4} - 7x + C$

17.

$f(x) = \int\limits(0.75 {x}^{3} - 7x - 2)dx = \frac{3}{4} \times \frac{ {x}^{4} }{4} - \frac{7 {x}^{2} }{2} - 2x + F = \\ = \frac{3 {x}^{4} }{16} - \frac{7 {x}^{2} }{2} - 2x + C$

18.

$f(x) = \int\limits(0.3 {x}^{10} + 2 {x}^{7} - 4x)dx = \\ = \frac{3}{10} \times \frac{ {x}^{11} }{11} + \frac{2 {x}^{8} }{8} - \frac{4 {x}^{2} }{2} + C= \\ = \frac{3 {x}^{11} }{110} + \frac{ {x}^{8} }{4} - 2 {x}^{2} + C$

19.

$f(x) = \int\limits(\sin(x) - \frac{1}{x} )dx = - \cos(x) - ln( |x| ) + C \\$

20.

$f(x) = \int\limits( 5\cos(x) - \frac{1}{x} ) dx= 5 \sin(x) - ln( |x| ) + C \\$

21.

$f(x) = \int\limits( - 4 {x}^{2} + {x}^{ - 7} + \sqrt{3} )dx = \\ = \frac{ - 4 {x}^{3} }{3} + \frac{ {x}^{ - 6} }{( - 6)} + \sqrt{3} x + C= \\ = - \frac{4 {x}^{3} }{3} - \frac{1}{6 {x}^{6} } + \sqrt{3}x + C$

22.

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

23.

$f(x) = \int\limits( {x}^{ - 5} + 3 {x}^{ - 2} - \frac{1}{4} {x}^{ - 3} - 1)dx = \\ = \frac{ {x}^{ - 4} }{ - 4} + \frac{3 {x}^{ - 1} }{( - 1)} - \frac{1}{4} \times \frac{ {x}^{ - 2} }{( - 2)} - x + C= \\ = - \frac{1}{4 {x}^{4} } - \frac{3}{x} + \frac{1}{8 {x}^{2} } - x + C$

24.

$f(x) = \int\limits( \frac{1}{2 \cos {}^{2} (x) } - \frac{1 }{3 \sin {}^{2}(x ) } + \frac{6}{x} )dx = \\ = 0.5tg(x) + \frac{1}{3}c tg (x) + 6 ln( |x| ) + C$

25.

$f(x) = \int\limits( \frac{1}{ \cos {}^{2} (x) } + {e}^{x} - 5 {x}^{2} - 1)dx = \\ = tg(x) + {e}^{x} - \frac{5 {x}^{3} }{3} - x + C$

26.

$f(x) = \int\limits( - \frac{1}{ \sin {}^{2} (x) } - {e}^{x} - 6 {x}^{4} + 3)dx = \\ = ctgx - {e}^{x} - \frac{6 {x}^{5} }{5} + 3x + C$

27.

$f(x) = \int\limits( - \frac{2}{ \sin {}^{2} (x) } - \frac{1}{x} + {x}^{3} - 6)dx = \\ = 2ctgx - ln( |x| ) + \frac{ {x}^{4} }{4} - 6x + C$

28.

$f(x) = \int\limits( - \frac{3}{ \cos {}^{2} (x) } + 4 {e}^{x} - {x}^{4} + 1)dx = \\ = - 3tgx + 4 {e}^{x} - \frac{ {x}^{5} }{5} + x + C$