Давайте аналитическая модель числового промежутка -4 < x < 3 постройте его модель и составьте соответствующую символическую запись. !

Х∈(-4;3)
геометрическая модель: на координатной прямой ставишь не закрашенные точки -4 и 3, между ними заштриховываешь интервал

Пошаговое объяснение:

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https://theshedcafe.com.au/uox/video-poi-v-mcg-fr04.html

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https://theshedcafe.com.au/uox/video-poi-v-mcg-gr02.html

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       x dx       1       2x dx         1       d(7+x²)        1

   ∫ =  ∫ = ∫ = ln(7+x²)+C

       7+x²      2        7+x²          2        7+x²           2  

                                 

[1/2 *ln(7+x²)+C ]¹= 1/2*[ 2x /(7+x²)+0]= x /(7+x²)

          x+18                (x-2)+20             1       2(x-2)                            dx

 2) ∫dx=∫ dx=  ∫ dx+20 ∫ =

        x²-4x-12            (x-2)²-16              2    (x-2)²-16                 (x-2)²-16   

     1                                          1          |  x-2-4    |           1                             5         | x-6  |

= *ln|(x-2)²-16|+20 * *ln || +C= *ln |x²-4x-12|+*ln || +C  

      2                                     2*8           |  x-2+4  |            2                             4         | x+2 |  

          

3) ∫(3-x) cosx dx=[ u=3-x , du=-dx ,  dv=cosx dx ,  v=sinx ] =(3-x)sinx+∫ sinx dx=

  =(3-x)sinx-cosx+C

   [(3-x)sinx-cosx]¹= -sinx+(3-x)cosx+sinx +0=(3-x)cosx