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Общий знаменатель (-log(sin(x)^2-1)/2)+log(sin(x))-1/(2*sin(x)^2)

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Вы ввели [src]
    /   2       \                           
-log\sin (x) - 1/                      1    
------------------ + log(sin(x)) - ---------
        2                               2   
                                   2*sin (x)
12(−1log⁡(sin⁡2(x)−1))+log⁡(sin⁡(x))−12sin⁡2(x)\frac{1}{2} \left(-1 \log{\left (\sin^{2}{\left (x \right )} - 1 \right )}\right) + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )}}
Степени [src]
                 /        2   \              
      1       log\-1 + sin (x)/              
- --------- - ----------------- + log(sin(x))
       2              2                      
  2*sin (x)
−12log⁡(sin⁡2(x)−1)+log⁡(sin⁡(x))−12sin⁡2(x)- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )}}
Численный ответ [src]
-0.5/sin(x)^2 - 0.5*log(sin(x)^2 - 1) + log(sin(x))
Рациональный знаменатель [src]
          2       /        2   \        2               
-2 - 2*sin (x)*log\-1 + sin (x)/ + 4*sin (x)*log(sin(x))
--------------------------------------------------------
                            2                           
                       4*sin (x)
14sin⁡2(x)(−2log⁡(sin⁡2(x)−1)sin⁡2(x)+4log⁡(sin⁡(x))sin⁡2(x)−2)\frac{1}{4 \sin^{2}{\left (x \right )}} \left(- 2 \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} \sin^{2}{\left (x \right )} + 4 \log{\left (\sin{\left (x \right )} \right )} \sin^{2}{\left (x \right )} - 2\right)
Объединение рациональных выражений [src]
        2    /     /        2   \                \
-1 + sin (x)*\- log\-1 + sin (x)/ + 2*log(sin(x))/
--------------------------------------------------
                         2                        
                    2*sin (x)
12sin⁡2(x)((−log⁡(sin⁡2(x)−1)+2log⁡(sin⁡(x)))sin⁡2(x)−1)\frac{1}{2 \sin^{2}{\left (x \right )}} \left(\left(- \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + 2 \log{\left (\sin{\left (x \right )} \right )}\right) \sin^{2}{\left (x \right )} - 1\right)
Общее упрощение [src]
                 /        2   \              
      1       log\-1 + sin (x)/              
- --------- - ----------------- + log(sin(x))
       2              2                      
  2*sin (x)
−12log⁡(sin⁡2(x)−1)+log⁡(sin⁡(x))−12sin⁡2(x)- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )}}
Собрать выражение [src]
         /  1   cos(2*x)\                         
      log|- - - --------|                         
  1      \  2      2    /   cos(2*x)              
- - - ------------------- + -------- + log(sin(x))
  4            2               4
−12log⁡(−12cos⁡(2x)−12)+log⁡(sin⁡(x))+14cos⁡(2x)−14- \frac{1}{2} \log{\left (- \frac{1}{2} \cos{\left (2 x \right )} - \frac{1}{2} \right )} + \log{\left (\sin{\left (x \right )} \right )} + \frac{1}{4} \cos{\left (2 x \right )} - \frac{1}{4}
     2         /        2   \              
  sin (x)   log\-1 + sin (x)/              
- ------- - ----------------- + log(sin(x))
     2              2
−12log⁡(sin⁡2(x)−1)+log⁡(sin⁡(x))−12sin⁡2(x)- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2} \sin^{2}{\left (x \right )}
Комбинаторика [src]
        2       /        2   \        2               
-1 - sin (x)*log\-1 + sin (x)/ + 2*sin (x)*log(sin(x))
------------------------------------------------------
                           2                          
                      2*sin (x)
12sin⁡2(x)(−log⁡(sin⁡2(x)−1)sin⁡2(x)+2log⁡(sin⁡(x))sin⁡2(x)−1)\frac{1}{2 \sin^{2}{\left (x \right )}} \left(- \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} \sin^{2}{\left (x \right )} + 2 \log{\left (\sin{\left (x \right )} \right )} \sin^{2}{\left (x \right )} - 1\right)
Общий знаменатель [src]
                 /        2   \              
      1       log\-1 + sin (x)/              
- --------- - ----------------- + log(sin(x))
       2              2                      
  2*sin (x)
−12log⁡(sin⁡2(x)−1)+log⁡(sin⁡(x))−12sin⁡2(x)- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )}}
Тригонометрическая часть [src]
                 /    2   \              
      1       log\-cos (x)/              
- --------- - ------------- + log(sin(x))
       2            2                    
  2*sin (x)
log⁡(sin⁡(x))−12log⁡(−cos⁡2(x))−12sin⁡2(x)\log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2} \log{\left (- \cos^{2}{\left (x \right )} \right )} - \frac{1}{2 \sin^{2}{\left (x \right )}}
Раскрыть выражение [src]
     2         /        2   \              
  sin (x)   log\-1 + sin (x)/              
- ------- - ----------------- + log(sin(x))
     2              2
−12log⁡(sin⁡2(x)−1)+log⁡(sin⁡(x))−12sin⁡2(x)- \frac{1}{2} \log{\left (\sin^{2}{\left (x \right )} - 1 \right )} + \log{\left (\sin{\left (x \right )} \right )} - \frac{1}{2} \sin^{2}{\left (x \right )}