2563*(sin(2*x)*1/2+x)*1/800-35*(x-sin(2*x)*1/2)*1/2-2563*sin(x)*1/200+211*cos(x)^2*1/25-422*cos(x)*1/25+2563*x*1/400 если x=2 (упростите выражение)

Выражение, которое надо упростить:

Решение

Вы ввели
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     /sin(2*x)    \      /    sin(2*x)\                                                  
2563*|-------- + x|   35*|x - --------|                        2                         
     \   2        /      \       2    /   2563*sin(x)   211*cos (x)   422*cos(x)   2563*x
------------------- - ----------------- - ----------- + ----------- - ---------- + ------
        800                   2               200            25           25        400  
$$\frac{2563 x}{400} + - \frac{35 x}{2} - \frac{35}{4} \sin{\left (2 x \right )} + \frac{2563}{800} \left(x + \frac{1}{2} \sin{\left (2 x \right )}\right) - \frac{2563}{200} \sin{\left (x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}$$
Подстановка условия
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(2563*(sin(2*x)/2 + x))/800 - 35*(x - sin(2*x)/2)/2 - 2563*sin(x)/200 + (211*cos(x)^2)/25 - 422*cos(x)/25 + (2563*x)/400 при x = 2
(2563*(sin(2*x)/2 + x))/800 - 35*(x - sin(2*x)/2)/2 - 2563*sin(x)/200 + (211*cos(x)^2)/25 - 422*cos(x)/25 + (2563*x)/400
$$\frac{2563 x}{400} + - \frac{35 x}{2} - \frac{35}{4} \sin{\left (2 x \right )} + \frac{2563}{800} \left(x + \frac{1}{2} \sin{\left (2 x \right )}\right) - \frac{2563}{200} \sin{\left (x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}$$
(2563*(sin(2*(2))/2 + (2)))/800 - 35*((2) - sin(2*(2))/2)/2 - 2563*sin((2))/200 + (211*cos((2))^2)/25 - 422*cos((2))/25 + (2563*(2))/400
$$\frac{2563 (2)}{400} + - \frac{35 (2)}{2} - \frac{35}{4} \sin{\left (2 (2) \right )} + \frac{2563}{800} \left((2) + \frac{1}{2} \sin{\left (2 (2) \right )}\right) - \frac{2563}{200} \sin{\left ((2) \right )} + \frac{211}{25} \cos^{2}{\left ((2) \right )} - \frac{422}{25} \cos{\left ((2) \right )}$$
(2563*(sin(2*2)/2 + 2))/800 - 35*(2 - sin(2*2)/2)/2 - 2563*sin(2)/200 + (211*cos(2)^2)/25 - 422*cos(2)/25 + (2563*2)/400
$$- - \frac{35}{4} \sin{\left (2 \cdot 2 \right )} + 35 + \frac{2563}{800} \left(\frac{1}{2} \sin{\left (2 \cdot 2 \right )} + 2\right) - \frac{2563}{200} \sin{\left (2 \right )} + \frac{211}{25} \cos^{2}{\left (2 \right )} - \frac{422}{25} \cos{\left (2 \right )} + \frac{5126}{400} 1$$
-6311/400 - 2563*sin(2)/200 - 422*cos(2)/25 + 211*cos(2)^2/25 + 16563*sin(4)/1600
$$- \frac{6311}{400} - \frac{2563}{200} \sin{\left (2 \right )} + \frac{16563}{1600} \sin{\left (4 \right )} + \frac{211}{25} \cos^{2}{\left (2 \right )} - \frac{422}{25} \cos{\left (2 \right )}$$
Степени
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                                             2                    
  6311*x   2563*sin(x)   422*cos(x)   211*cos (x)   16563*sin(2*x)
- ------ - ----------- - ---------- + ----------- + --------------
   800         200           25            25            1600     
$$- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}$$
Численный ответ
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10.351875*sin(2*x) + 8.44*cos(x)^2 - 7.88875*x - 16.88*cos(x) - 12.815*sin(x)
Рациональный знаменатель
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                                             2                    
  6311*x   2563*sin(x)   422*cos(x)   211*cos (x)   16563*sin(2*x)
- ------ - ----------- - ---------- + ----------- + --------------
   800         200           25            25            1600     
$$- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}$$
Объединение рациональных выражений
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                                                  2                    
-27008*cos(x) - 20504*sin(x) - 12622*x + 13504*cos (x) + 16563*sin(2*x)
-----------------------------------------------------------------------
                                  1600                                 
$$\frac{1}{1600} \left(- 12622 x - 20504 \sin{\left (x \right )} + 16563 \sin{\left (2 x \right )} + 13504 \cos^{2}{\left (x \right )} - 27008 \cos{\left (x \right )}\right)$$
Общее упрощение
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                                             2                    
  6311*x   2563*sin(x)   422*cos(x)   211*cos (x)   16563*sin(2*x)
- ------ - ----------- - ---------- + ----------- + --------------
   800         200           25            25            1600     
$$- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}$$
Собрать выражение
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                            /sin(2*x)    \      /    sin(2*x)\                           
       2               2563*|-------- + x|   35*|x - --------|                           
211*cos (x)   2563*x        \   2        /      \       2    /   422*cos(x)   2563*sin(x)
----------- + ------ + ------------------- - ----------------- - ---------- - -----------
     25        400             800                   2               25           200    
$$\frac{2563 x}{400} - \frac{35 x}{2} - \frac{35}{4} \sin{\left (2 x \right )} + \frac{2563}{800} \left(x + \frac{1}{2} \sin{\left (2 x \right )}\right) - \frac{2563}{200} \sin{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )}$$
211   6311*x   2563*sin(x)   422*cos(x)   211*cos(2*x)   16563*sin(2*x)
--- - ------ - ----------- - ---------- + ------------ + --------------
 50    800         200           25            50             1600     
$$- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} - \frac{422}{25} \cos{\left (x \right )} + \frac{211}{50} \cos{\left (2 x \right )} + \frac{211}{50}$$
Общий знаменатель
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                                             2                    
  6311*x   2563*sin(x)   422*cos(x)   211*cos (x)   16563*sin(2*x)
- ------ - ----------- - ---------- + ----------- + --------------
   800         200           25            25            1600     
$$- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}$$
Комбинаторика
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 /                           2                                           \ 
-\-16563*sin(2*x) - 13504*cos (x) + 12622*x + 20504*sin(x) + 27008*cos(x)/ 
---------------------------------------------------------------------------
                                    1600                                   
$$- \frac{1}{1600} \left(12622 x + 20504 \sin{\left (x \right )} - 16563 \sin{\left (2 x \right )} - 13504 \cos^{2}{\left (x \right )} + 27008 \cos{\left (x \right )}\right)$$
Тригонометрическая часть
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211   6311*x   2563*sin(x)   422*cos(x)   211*cos(2*x)   16563*sin(2*x)
--- - ------ - ----------- - ---------- + ------------ + --------------
 50    800         200           25            50             1600     
$$- \frac{6311 x}{800} - \frac{2563}{200} \sin{\left (x \right )} + \frac{16563}{1600} \sin{\left (2 x \right )} - \frac{422}{25} \cos{\left (x \right )} + \frac{211}{50} \cos{\left (2 x \right )} + \frac{211}{50}$$
Раскрыть выражение
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                                             2                         
  6311*x   2563*sin(x)   422*cos(x)   211*cos (x)   16563*cos(x)*sin(x)
- ------ - ----------- - ---------- + ----------- + -------------------
   800         200           25            25               800        
$$- \frac{6311 x}{800} + \frac{16563}{800} \sin{\left (x \right )} \cos{\left (x \right )} - \frac{2563}{200} \sin{\left (x \right )} + \frac{211}{25} \cos^{2}{\left (x \right )} - \frac{422}{25} \cos{\left (x \right )}$$