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Общий знаменатель (-log(cos(x)+1)/4)+log(co ... )/4+cos(x)/(2*cos(x)^2-2)

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Примеры

Решение

Вы ввели [src]
-log(cos(x) + 1)    log(cos(x) - 1)       cos(x)   
----------------- + --------------- + -------------
        4                  4               2       
                                      2*cos (x) - 2
$$\frac{1}{4} \log{\left (\cos{\left (x \right )} - 1 \right )} + \frac{1}{4} \left(-1 \log{\left (\cos{\left (x \right )} + 1 \right )}\right) + \frac{\cos{\left (x \right )}}{2 \cos^{2}{\left (x \right )} - 2}$$
Степени [src]
  log(1 + cos(x))   log(-1 + cos(x))       cos(x)    
- --------------- + ---------------- + --------------
         4                 4                     2   
                                       -2 + 2*cos (x)
$$\frac{1}{4} \log{\left (\cos{\left (x \right )} - 1 \right )} - \frac{1}{4} \log{\left (\cos{\left (x \right )} + 1 \right )} + \frac{\cos{\left (x \right )}}{2 \cos^{2}{\left (x \right )} - 2}$$
Численный ответ [src]
0.25*log(cos(x) - 1) - 0.25*log(cos(x) + 1) + cos(x)/(-2.0 + 2.0*cos(x)^2)
Рациональный знаменатель [src]
                                  2                          2                                     
-log(-1 + cos(x)) + 2*cos(x) + cos (x)*log(-1 + cos(x)) - cos (x)*log(1 + cos(x)) + log(1 + cos(x))
---------------------------------------------------------------------------------------------------
                                                     2                                             
                                           -4 + 4*cos (x)
$$\frac{1}{4 \cos^{2}{\left (x \right )} - 4} \left(\log{\left (\cos{\left (x \right )} - 1 \right )} \cos^{2}{\left (x \right )} - \log{\left (\cos{\left (x \right )} - 1 \right )} - \log{\left (\cos{\left (x \right )} + 1 \right )} \cos^{2}{\left (x \right )} + \log{\left (\cos{\left (x \right )} + 1 \right )} + 2 \cos{\left (x \right )}\right)$$
Объединение рациональных выражений [src]
           /        2   \                                      
2*cos(x) + \-1 + cos (x)/*(-log(1 + cos(x)) + log(-1 + cos(x)))
---------------------------------------------------------------
                          /        2   \                       
                        4*\-1 + cos (x)/
$$\frac{1}{4 \cos^{2}{\left (x \right )} - 4} \left(\left(\log{\left (\cos{\left (x \right )} - 1 \right )} - \log{\left (\cos{\left (x \right )} + 1 \right )}\right) \left(\cos^{2}{\left (x \right )} - 1\right) + 2 \cos{\left (x \right )}\right)$$
Общее упрощение [src]
  log(1 + cos(x))   log(-1 + cos(x))     cos(x) 
- --------------- + ---------------- - ---------
         4                 4                2   
                                       2*sin (x)
$$\frac{1}{4} \log{\left (\cos{\left (x \right )} - 1 \right )} - \frac{1}{4} \log{\left (\cos{\left (x \right )} + 1 \right )} - \frac{\cos{\left (x \right )}}{2 \sin^{2}{\left (x \right )}}$$
Собрать выражение [src]
  log(1 + cos(x))   log(-1 + cos(x))       cos(x)   
- --------------- + ---------------- + -------------
         4                 4           -1 + cos(2*x)
$$\frac{1}{4} \log{\left (\cos{\left (x \right )} - 1 \right )} - \frac{1}{4} \log{\left (\cos{\left (x \right )} + 1 \right )} + \frac{\cos{\left (x \right )}}{\cos{\left (2 x \right )} - 1}$$
  log(1 + cos(x))   log(-1 + cos(x))       cos(x)    
- --------------- + ---------------- + --------------
         4                 4                     2   
                                       -2 + 2*cos (x)
$$\frac{1}{4} \log{\left (\cos{\left (x \right )} - 1 \right )} - \frac{1}{4} \log{\left (\cos{\left (x \right )} + 1 \right )} + \frac{\cos{\left (x \right )}}{2 \cos^{2}{\left (x \right )} - 2}$$
Комбинаторика [src]
 /                                 2                         2                                       \ 
-\-log(1 + cos(x)) - 2*cos(x) + cos (x)*log(1 + cos(x)) - cos (x)*log(-1 + cos(x)) + log(-1 + cos(x))/ 
-------------------------------------------------------------------------------------------------------
                                      4*(1 + cos(x))*(-1 + cos(x))
$$- \frac{1}{4 \left(\cos{\left (x \right )} - 1\right) \left(\cos{\left (x \right )} + 1\right)} \left(- \log{\left (\cos{\left (x \right )} - 1 \right )} \cos^{2}{\left (x \right )} + \log{\left (\cos{\left (x \right )} - 1 \right )} + \log{\left (\cos{\left (x \right )} + 1 \right )} \cos^{2}{\left (x \right )} - \log{\left (\cos{\left (x \right )} + 1 \right )} - 2 \cos{\left (x \right )}\right)$$
Общий знаменатель [src]
  log(1 + cos(x))   log(-1 + cos(x))       cos(x)    
- --------------- + ---------------- + --------------
         4                 4                     2   
                                       -2 + 2*cos (x)
$$\frac{1}{4} \log{\left (\cos{\left (x \right )} - 1 \right )} - \frac{1}{4} \log{\left (\cos{\left (x \right )} + 1 \right )} + \frac{\cos{\left (x \right )}}{2 \cos^{2}{\left (x \right )} - 2}$$
Тригонометрическая часть [src]
  log(1 + cos(x))   log(-1 + cos(x))     cos(x) 
- --------------- + ---------------- - ---------
         4                 4                2   
                                       2*sin (x)
$$\frac{1}{4} \log{\left (\cos{\left (x \right )} - 1 \right )} - \frac{1}{4} \log{\left (\cos{\left (x \right )} + 1 \right )} - \frac{\cos{\left (x \right )}}{2 \sin^{2}{\left (x \right )}}$$
Раскрыть выражение [src]
  log(1 + cos(x))   log(-1 + cos(x))       cos(x)    
- --------------- + ---------------- + --------------
         4                 4                     2   
                                       -2 + 2*cos (x)
$$\frac{1}{4} \log{\left (\cos{\left (x \right )} - 1 \right )} - \frac{1}{4} \log{\left (\cos{\left (x \right )} + 1 \right )} + \frac{\cos{\left (x \right )}}{2 \cos^{2}{\left (x \right )} - 2}$$