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

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Примеры

Решение

Вы ввели [src]
                                          2     
   /   2         \          1          sin (2*x)
log\sin (2*x) - 1/ - --------------- + ---------
                          2                2    
                     2*sin (2*x) - 2            
------------------------------------------------
                       2
$$\frac{1}{2} \left(\log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} - \frac{1}{2 \sin^{2}{\left (2 x \right )} - 2} + \frac{1}{2} \sin^{2}{\left (2 x \right )}\right)$$
Степени [src]
   /        2     \                             2     
log\-1 + sin (2*x)/            1             sin (2*x)
------------------- - -------------------- + ---------
         2              /          2     \       4    
                      2*\-2 + 2*sin (2*x)/
$$\frac{1}{2} \log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} + \frac{1}{4} \sin^{2}{\left (2 x \right )} - \frac{1}{4 \sin^{2}{\left (2 x \right )} - 4}$$
Численный ответ [src]
0.25*sin(2*x)^2 + 0.5*log(sin(2*x)^2 - 1) - 0.5/(-2.0 + 2.0*sin(2*x)^2)
Рациональный знаменатель [src]
        4           2             /        2     \        2         /        2     \
-1 + sin (2*x) - sin (2*x) - 2*log\-1 + sin (2*x)/ + 2*sin (2*x)*log\-1 + sin (2*x)/
------------------------------------------------------------------------------------
                                            2                                       
                                  -4 + 4*sin (2*x)
$$\frac{1}{4 \sin^{2}{\left (2 x \right )} - 4} \left(2 \log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} \sin^{2}{\left (2 x \right )} - 2 \log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} + \sin^{4}{\left (2 x \right )} - \sin^{2}{\left (2 x \right )} - 1\right)$$
Объединение рациональных выражений [src]
        2      /        2     \     /        2     \    /        2     \
-1 + sin (2*x)*\-1 + sin (2*x)/ + 2*\-1 + sin (2*x)/*log\-1 + sin (2*x)/
------------------------------------------------------------------------
                             /        2     \                           
                           4*\-1 + sin (2*x)/
$$\frac{1}{4 \sin^{2}{\left (2 x \right )} - 4} \left(2 \left(\sin^{2}{\left (2 x \right )} - 1\right) \log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} + \left(\sin^{2}{\left (2 x \right )} - 1\right) \sin^{2}{\left (2 x \right )} - 1\right)$$
Общее упрощение [src]
     /        2     \ /   2             /        2     \\
-1 + \-1 + sin (2*x)/*\sin (2*x) + 2*log\-1 + sin (2*x)//
---------------------------------------------------------
                      /        2     \                   
                    4*\-1 + sin (2*x)/
$$\frac{1}{4 \sin^{2}{\left (2 x \right )} - 4} \left(\left(2 \log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} + \sin^{2}{\left (2 x \right )}\right) \left(\sin^{2}{\left (2 x \right )} - 1\right) - 1\right)$$
Собрать выражение [src]
                    /  1   cos(4*x)\                 /  1   cos(4*x)\
9 - cos(8*x) + 8*log|- - - --------| + 8*cos(4*x)*log|- - - --------|
                    \  2      2    /                 \  2      2    /
---------------------------------------------------------------------
                           16 + 16*cos(4*x)
$$\frac{1}{16 \cos{\left (4 x \right )} + 16} \left(8 \log{\left (- \frac{1}{2} \cos{\left (4 x \right )} - \frac{1}{2} \right )} \cos{\left (4 x \right )} + 8 \log{\left (- \frac{1}{2} \cos{\left (4 x \right )} - \frac{1}{2} \right )} - \cos{\left (8 x \right )} + 9\right)$$
                    /                2\             /        /                2\\
        4           |/        2     \ |      2      |        |/        2     \ ||
-1 + sin (2*x) - log\\-1 + sin (2*x)/ / + sin (2*x)*\-1 + log\\-1 + sin (2*x)/ //
---------------------------------------------------------------------------------
                                           2                                     
                                 -4 + 4*sin (2*x)
$$\frac{1}{4 \sin^{2}{\left (2 x \right )} - 4} \left(\left(\log{\left (\left(\sin^{2}{\left (2 x \right )} - 1\right)^{2} \right )} - 1\right) \sin^{2}{\left (2 x \right )} - \log{\left (\left(\sin^{2}{\left (2 x \right )} - 1\right)^{2} \right )} + \sin^{4}{\left (2 x \right )} - 1\right)$$
   /   2         \                            2     
log\sin (2*x) - 1/            1            sin (2*x)
------------------ - ------------------- + ---------
        2              /     2         \      2*2   
                     2*\2*sin (2*x) - 2/
$$\frac{1}{2} \log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} + \frac{1}{4} \sin^{2}{\left (2 x \right )} - \frac{1}{4 \sin^{2}{\left (2 x \right )} - 4}$$
Общий знаменатель [src]
   /        2     \                         2     
log\-1 + sin (2*x)/          1           sin (2*x)
------------------- - ---------------- + ---------
         2                      2            4    
                      -4 + 4*sin (2*x)
$$\frac{1}{2} \log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} + \frac{1}{4} \sin^{2}{\left (2 x \right )} - \frac{1}{4 \sin^{2}{\left (2 x \right )} - 4}$$
Комбинаторика [src]
        4           2             /        2     \        2         /        2     \
-1 + sin (2*x) - sin (2*x) - 2*log\-1 + sin (2*x)/ + 2*sin (2*x)*log\-1 + sin (2*x)/
------------------------------------------------------------------------------------
                          4*(1 + sin(2*x))*(-1 + sin(2*x))
$$\frac{1}{4 \left(\sin{\left (2 x \right )} - 1\right) \left(\sin{\left (2 x \right )} + 1\right)} \left(2 \log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} \sin^{2}{\left (2 x \right )} - 2 \log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} + \sin^{4}{\left (2 x \right )} - \sin^{2}{\left (2 x \right )} - 1\right)$$
Тригонометрическая часть [src]
                      /   2         \      2     
       1           log\sin (2*x) - 1/   sin (2*x)
---------------- + ------------------ + ---------
2*(1 + cos(4*x))           2                4
$$\frac{1}{2} \log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} + \frac{1}{4} \sin^{2}{\left (2 x \right )} + \frac{1}{2 \cos{\left (4 x \right )} + 2}$$
Раскрыть выражение [src]
   /        2     \                             2     
log\-1 + sin (2*x)/            1             sin (2*x)
------------------- - -------------------- + ---------
         2              /          2     \       4    
                      2*\-2 + 2*sin (2*x)/
$$\frac{1}{2} \log{\left (\sin^{2}{\left (2 x \right )} - 1 \right )} + \frac{1}{4} \sin^{2}{\left (2 x \right )} - \frac{1}{4 \sin^{2}{\left (2 x \right )} - 4}$$
   /          2       2   \                                               
log\-1 + 4*cos (x)*sin (x)/               1                   2       2   
--------------------------- - -------------------------- + cos (x)*sin (x)
             2                  /          2       2   \                  
                              2*\-2 + 8*cos (x)*sin (x)/
$$\frac{1}{2} \log{\left (4 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} - 1 \right )} + \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} - \frac{1}{16 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} - 4}$$