Найдите первообразные следующих функций:№11) f(x) = 3x; 2) f(x) = 4x2 + x – 2; 3) f(x) = + 1; 4) f(x) = №2.1. f(x) = 2sinx; 2) f(x) = 5cosx; 3) f(x) = 3cosx - 4sinx; 4)f(x) = 5sinx + 2 cosx; 5) f(x) = x2 + ; 6) f(x) = x3 - ; 7) f(x) = sin(3x + ); 8) f(x) = cos(2x + ).

Question

Fothris

5 год назад

ОТВЕТЫ

Genoveva

Nov 28, 2020

1.

$1)∫3xdx =\frac{3 {x}^{2} }{2}+ c$

$2)∫(4 {x}^{2}+ x - 2)dx =\frac{4 {x}^{3} }{3}+\frac{ {x}^{2} }{2} - 2x + c$

$3)∫( \frac{ {x}^{3} }{3}+ 1)dx =\frac{ {x}^{4} }{12}+ x + c$

$4)∫ {x}^{ - 2} dx =\frac{ {x}^{ - 1} }{ - 1}+ c =-\frac{1}{x}+ c$

2.

$1)∫2 \sin(x) dx =-2\cos(x)+ c$

$2)∫5 \cos(x) dx = 5 \sin(x)+ c$

$3)∫(3 \cos(x)- 4 \sin(x) )dx = 3 \sin(x)+ 4 \cos(x)+ c$

$4)∫(5 \sin(x)+ 2 \cos(x) )dx =- 5 \cos(x)+ 2 \sin(x)+ c$

$5)∫( {x}^{2}+ 3 {x}^{ -\frac{1}{2} } )dx =\frac{ {x}^{3} }{3}+ 3 \frac{ {x}^{ \frac{1}{2} } }{ \frac{1}{2} }+ c =\frac{ {x}^{3} }{3}+ 6 \sqrt{x}+ c$

$6)∫( {x}^{3}- 4 {x}^{ -\frac{1}{2} } )dx =\frac{ {x}^{4} }{4}- 8 \sqrt{x}+ c$

$7)∫ \sin( x+\frac{\pi}{3} ) dx = ∫ \sin(x +\frac{\pi}{3} ) d(x +\frac{\pi}{3}==-\cos(x +\frac{\pi}{3} )+ c$

$8)∫ \cos(2x +\frac{\pi}{6} ) dx =\frac{1}{2} ∫ \cos(2x +\frac{\pi}{6} ) d(2x +\frac{\pi}{6} ) =\frac{1}{2}\sin(2x +\frac{\pi}{6} )+ c$

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