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

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Вы ввели [src]
           2                                                   
          x                                                    
        ----- //    2           \                  2          \
        x + 1 ||  -x        2*x |                 x *sin(x)   |
(cos(x))     *||-------- + -----|*log(cos(x)) - --------------|
              ||       2   x + 1|               (x + 1)*cos(x)|
              \\(x + 1)         /                             /
$$\left(- x^{2} \frac{1}{\left(x + 1\right) \cos{\left (x \right )}} \sin{\left (x \right )} + \left(\frac{2 x}{x + 1} + \frac{-1 x^{2}}{\left(x + 1\right)^{2}}\right) \log{\left (\cos{\left (x \right )} \right )}\right) \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )}$$
Степени [src]
           2                                                     
          x                                                      
        ----- //      2           \                  2          \
        1 + x ||     x        2*x |                 x *sin(x)   |
(cos(x))     *||- -------- + -----|*log(cos(x)) - --------------|
              ||         2   1 + x|               (1 + x)*cos(x)|
              \\  (1 + x)         /                             /
$$\left(- \frac{x^{2} \sin{\left (x \right )}}{\left(x + 1\right) \cos{\left (x \right )}} + \left(- \frac{x^{2}}{\left(x + 1\right)^{2}} + \frac{2 x}{x + 1}\right) \log{\left (\cos{\left (x \right )} \right )}\right) \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )}$$
Численный ответ [src]
cos(x)^(x^2/(1.0 + x))*((2.0*x/(1.0 + x) - 1.0*x^2/(1.0 + x)^2)*log(cos(x)) - x^2*sin(x)/((1.0 + x)*cos(x)))
Рациональный знаменатель [src]
           2                                                                                   
          x                                                                                    
        -----                                                                                  
        x + 1 /   2        3                  /   2                      2\                   \
(cos(x))     *\- x *(1 + x) *sin(x) + (1 + x)*\- x *(1 + x) + 2*x*(1 + x) /*cos(x)*log(cos(x))/
-----------------------------------------------------------------------------------------------
                                               4                                               
                                        (1 + x) *cos(x)
$$\frac{\cos^{\frac{x^{2}}{x + 1}}{\left (x \right )}}{\left(x + 1\right)^{4} \cos{\left (x \right )}} \left(- x^{2} \left(x + 1\right)^{3} \sin{\left (x \right )} + \left(x + 1\right) \left(- x^{2} \left(x + 1\right) + 2 x \left(x + 1\right)^{2}\right) \log{\left (\cos{\left (x \right )} \right )} \cos{\left (x \right )}\right)$$
Объединение рациональных выражений [src]
             2                                                 
            x                                                  
          -----                                                
          1 + x                                                
x*(cos(x))     *((2 + x)*cos(x)*log(cos(x)) - x*(1 + x)*sin(x))
---------------------------------------------------------------
                               2                               
                        (1 + x) *cos(x)
$$\frac{x \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )}}{\left(x + 1\right)^{2} \cos{\left (x \right )}} \left(- x \left(x + 1\right) \sin{\left (x \right )} + \left(x + 2\right) \log{\left (\cos{\left (x \right )} \right )} \cos{\left (x \right )}\right)$$
Общее упрощение [src]
                2                                                    
          -1 + x  - x                                                
          -----------                                                
             1 + x                                                   
x*(cos(x))           *((2 + x)*cos(x)*log(cos(x)) - x*(1 + x)*sin(x))
---------------------------------------------------------------------
                                      2                              
                               (1 + x)
$$\frac{x}{\left(x + 1\right)^{2}} \left(- x \left(x + 1\right) \sin{\left (x \right )} + \left(x + 2\right) \log{\left (\cos{\left (x \right )} \right )} \cos{\left (x \right )}\right) \cos^{\frac{x^{2} - x - 1}{x + 1}}{\left (x \right )}$$
Собрать выражение [src]
             2                                                       2                  
            x                                                       x                   
          -----                                               1 + -----                 
          1 + x /       /   2   \    2            \               1 + x / 2    3\       
- (cos(x))     *\- x*log\cos (x)/ - x *log(cos(x))/ - (cos(x))         *\x  + x /*sin(x)
----------------------------------------------------------------------------------------
                                           2                                            
                                      1 + x  + 2*x
$$\frac{1}{x^{2} + 2 x + 1} \left(- \left(x^{3} + x^{2}\right) \sin{\left (x \right )} \cos^{\frac{x^{2}}{x + 1} + 1}{\left (x \right )} - \left(- x^{2} \log{\left (\cos{\left (x \right )} \right )} - x \log{\left (\cos^{2}{\left (x \right )} \right )}\right) \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )}\right)$$
           2                                                                          
          x                                                                           
        ----- /    2                3                 2                              \
        1 + x |   x *sin(2*x)      x *sin(2*x)     2*x *log(cos(x))   4*x*log(cos(x))|
(cos(x))     *|- -------------- - -------------- + ---------------- + ---------------|
              |         2                2                 2                  2      |
              \  2 + 2*x  + 4*x   2 + 2*x  + 4*x    2 + 2*x  + 4*x     2 + 2*x  + 4*x/
$$\left(- \frac{x^{3} \sin{\left (2 x \right )}}{2 x^{2} + 4 x + 2} + \frac{2 x^{2} \log{\left (\cos{\left (x \right )} \right )}}{2 x^{2} + 4 x + 2} - \frac{x^{2} \sin{\left (2 x \right )}}{2 x^{2} + 4 x + 2} + \frac{4 x \log{\left (\cos{\left (x \right )} \right )}}{2 x^{2} + 4 x + 2}\right) \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )}$$
Общий знаменатель [src]
                                          2                         2                      2                    
           2                             x                         x                      x                     
          x                            -----                     -----                  -----                   
        -----                2         1 + x           3         1 + x                  1 + x                   
        1 + x               x *(cos(x))     *sin(x) + x *(cos(x))     *sin(x) + (cos(x))     *cos(x)*log(cos(x))
(cos(x))     *log(cos(x)) - ------------------------------------------------------------------------------------
                                                       2                                                        
                                                      x *cos(x) + 2*x*cos(x) + cos(x)
$$\log{\left (\cos{\left (x \right )} \right )} \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )} - \frac{1}{x^{2} \cos{\left (x \right )} + 2 x \cos{\left (x \right )} + \cos{\left (x \right )}} \left(x^{3} \sin{\left (x \right )} \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )} + x^{2} \sin{\left (x \right )} \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )} + \log{\left (\cos{\left (x \right )} \right )} \cos{\left (x \right )} \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )}\right)$$
Тригонометрическая часть [src]
           2                                              
          x                                               
        ----- //    2           \                2       \
        x + 1 ||  -x        2*x |               x *tan(x)|
(cos(x))     *||-------- + -----|*log(cos(x)) - ---------|
              ||       2   x + 1|                 1 + x  |
              \\(x + 1)         /                        /
$$\left(- \frac{x^{2} \tan{\left (x \right )}}{x + 1} + \left(\frac{2 x}{x + 1} + \frac{-1 x^{2}}{\left(x + 1\right)^{2}}\right) \log{\left (\cos{\left (x \right )} \right )}\right) \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )}$$
Комбинаторика [src]
              2                                                                       
             x                                                                        
           -----                                                                      
           1 + x /            2                                                     \ 
-x*(cos(x))     *\x*sin(x) + x *sin(x) - 2*cos(x)*log(cos(x)) - x*cos(x)*log(cos(x))/ 
--------------------------------------------------------------------------------------
                                          2                                           
                                   (1 + x) *cos(x)
$$- \frac{x \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )}}{\left(x + 1\right)^{2} \cos{\left (x \right )}} \left(x^{2} \sin{\left (x \right )} - x \log{\left (\cos{\left (x \right )} \right )} \cos{\left (x \right )} + x \sin{\left (x \right )} - 2 \log{\left (\cos{\left (x \right )} \right )} \cos{\left (x \right )}\right)$$
Раскрыть выражение [src]
           2                                                   
          x                                                    
        ----- //    2           \                  2          \
        x + 1 ||  -x        2*x |                 x *sin(x)   |
(cos(x))     *||-------- + -----|*log(cos(x)) - --------------|
              ||       2   x + 1|               (x + 1)*cos(x)|
              \\(x + 1)         /                             /
$$\left(- \frac{x^{2} \sin{\left (x \right )}}{\left(x + 1\right) \cos{\left (x \right )}} + \left(\frac{2 x}{x + 1} + \frac{-1 x^{2}}{\left(x + 1\right)^{2}}\right) \log{\left (\cos{\left (x \right )} \right )}\right) \cos^{\frac{x^{2}}{x + 1}}{\left (x \right )}$$