(-5-5*cot(5*x+2)^2)*(6*x^ ... ^3*cot(5*x+2) если x=-1/2 (упростите выражение)

Вы ввели

/          2         \ /   4    \       3             
\-5 - 5*cot (5*x + 2)/*\6*x  + 7/ + 24*x *cot(5*x + 2)

$$24 x^{3} \cot{\left (5 x + 2 \right )} + \left(6 x^{4} + 7\right) \left(- 5 \cot^{2}{\left (5 x + 2 \right )} - 5\right)$$

Подстановка условия

(-5 - 5*cot(5*x + 2)^2)*(6*x^4 + 7) + (24*x^3)*cot(5*x + 2) при x = -1/2

(-5 - 5*cot(5*x + 2)^2)*(6*x^4 + 7) + (24*x^3)*cot(5*x + 2)

$$24 x^{3} \cot{\left (5 x + 2 \right )} + \left(6 x^{4} + 7\right) \left(-1 \cdot 5 \cot^{2}{\left (5 x + 2 \right )} - 5\right)$$

(-5 - 5*cot(5*(-1/2) + 2)^2)*(6*(-1/2)^4 + 7) + (24*(-1/2)^3)*cot(5*(-1/2) + 2)

$$24 (-1/2)^{3} \cot{\left (5 (-1/2) + 2 \right )} + \left(6 (-1/2)^{4} + 7\right) \left(-1 \cdot 5 \cot^{2}{\left (5 (-1/2) + 2 \right )} - 5\right)$$

(-5 - 5*cot(5*(-1)/2 + 2)^2)*(6*(-1/2)^4 + 7) + (24*(-1/2)^3)*cot(5*(-1)/2 + 2)

$$\left(6 \left(- \frac{1}{2}\right)^{4} + 7\right) \left(-1 \cdot 5 \cot^{2}{\left (\frac{-5}{2} + 2 \right )} - 5\right) + 24 \left(- \frac{1}{2}\right)^{3} \cot{\left (\frac{-5}{2} + 2 \right )}$$

-295/8 + 3*cot(1/2) - 295*cot(1/2)^2/8

$$- \frac{295}{8} \cot^{2}{\left (\frac{1}{2} \right )} - \frac{295}{8} + 3 \cot{\left (\frac{1}{2} \right )}$$

Численный ответ

(7.0 + 6.0*x^4)*(-5.0 - 5.0*cot(5*x + 2)^2) + 24.0*x^3*cot(5*x + 2)

Рациональный знаменатель

            2                4       4    2                3             
-35 - 35*cot (2 + 5*x) - 30*x  - 30*x *cot (2 + 5*x) + 24*x *cot(2 + 5*x)

$$- 30 x^{4} \cot^{2}{\left (5 x + 2 \right )} - 30 x^{4} + 24 x^{3} \cot{\left (5 x + 2 \right )} - 35 \cot^{2}{\left (5 x + 2 \right )} - 35$$

Объединение рациональных выражений

  /        2         \ /       4\       3             
5*\-1 - cot (2 + 5*x)/*\7 + 6*x / + 24*x *cot(2 + 5*x)

$$24 x^{3} \cot{\left (5 x + 2 \right )} + 5 \left(6 x^{4} + 7\right) \left(- \cot^{2}{\left (5 x + 2 \right )} - 1\right)$$

Общее упрощение

     /       4\                     
   5*\7 + 6*x /       3             
- ------------- + 24*x *cot(2 + 5*x)
     2                              
  sin (2 + 5*x)                     

$$24 x^{3} \cot{\left (5 x + 2 \right )} - \frac{30 x^{4} + 35}{\sin^{2}{\left (5 x + 2 \right )}}$$

Собрать выражение

        2                4    2                3             
- 35*csc (2 + 5*x) - 30*x *csc (2 + 5*x) + 24*x *cot(2 + 5*x)

$$- 30 x^{4} \csc^{2}{\left (5 x + 2 \right )} + 24 x^{3} \cot{\left (5 x + 2 \right )} - 35 \csc^{2}{\left (5 x + 2 \right )}$$

Общий знаменатель

            2                4       4    2                3             
-35 - 35*cot (2 + 5*x) - 30*x  - 30*x *cot (2 + 5*x) + 24*x *cot(2 + 5*x)

$$- 30 x^{4} \cot^{2}{\left (5 x + 2 \right )} - 30 x^{4} + 24 x^{3} \cot{\left (5 x + 2 \right )} - 35 \cot^{2}{\left (5 x + 2 \right )} - 35$$

Тригонометрическая часть

           4                      
 -35 - 30*x         3             
------------- + 24*x *cot(5*x + 2)
   2                              
sin (2 + 5*x)                     

$$24 x^{3} \cot{\left (5 x + 2 \right )} + \frac{- 30 x^{4} - 35}{\sin^{2}{\left (5 x + 2 \right )}}$$

Комбинаторика

            2                4       4    2                3             
-35 - 35*cot (2 + 5*x) - 30*x  - 30*x *cot (2 + 5*x) + 24*x *cot(2 + 5*x)

$$- 30 x^{4} \cot^{2}{\left (5 x + 2 \right )} - 30 x^{4} + 24 x^{3} \cot{\left (5 x + 2 \right )} - 35 \cot^{2}{\left (5 x + 2 \right )} - 35$$

Раскрыть выражение

/                             2\                  3                       
|     5*(-1 + cot(2)*cot(5*x)) | /       4\   24*x *(-1 + cot(2)*cot(5*x))
|-5 - -------------------------|*\7 + 6*x / + ----------------------------
|                           2  |                   cot(2) + cot(5*x)      
\        (cot(2) + cot(5*x))   /                                          

$$\frac{24 x^{3} \left(\cot{\left (2 \right )} \cot{\left (5 x \right )} - 1\right)}{\cot{\left (5 x \right )} + \cot{\left (2 \right )}} + \left(6 x^{4} + 7\right) \left(- \frac{5 \left(\cot{\left (2 \right )} \cot{\left (5 x \right )} - 1\right)^{2}}{\left(\cot{\left (5 x \right )} + \cot{\left (2 \right )}\right)^{2}} - 5\right)$$