Общий знаменатель pi*sin(n)/n-((n^2-2)*sin(n)+2*n*cos(n))/(pi*n^3)

Выражение, которое надо упростить:

Решение

Вы ввели
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            / 2    \                    
pi*sin(n)   \n  - 2/*sin(n) + 2*n*cos(n)
--------- - ----------------------------
    n                      3            
                       pi*n             
$$- \frac{1}{\pi n^{3}} \left(2 n \cos{\left (n \right )} + \left(n^{2} - 2\right) \sin{\left (n \right )}\right) + \frac{\pi}{n} \sin{\left (n \right )}$$
Степени
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              /      2\                    
pi*sin(n)   - \-2 + n /*sin(n) - 2*n*cos(n)
--------- + -------------------------------
    n                        3             
                         pi*n              
$$\frac{\pi}{n} \sin{\left (n \right )} + \frac{1}{\pi n^{3}} \left(- 2 n \cos{\left (n \right )} - \left(n^{2} - 2\right) \sin{\left (n \right )}\right)$$
            /      2\                    
pi*sin(n)   \-2 + n /*sin(n) + 2*n*cos(n)
--------- - -----------------------------
    n                       3            
                        pi*n             
$$\frac{\pi}{n} \sin{\left (n \right )} - \frac{1}{\pi n^{3}} \left(2 n \cos{\left (n \right )} + \left(n^{2} - 2\right) \sin{\left (n \right )}\right)$$
Численный ответ
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3.14159265358979*sin(n)/n - 0.318309886183791*((-2.0 + n^2)*sin(n) + 2.0*n*cos(n))/n^3
Объединение рациональных выражений
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  /      2\                         2  2       
- \-2 + n /*sin(n) - 2*n*cos(n) + pi *n *sin(n)
-----------------------------------------------
                         3                     
                     pi*n                      
$$\frac{1}{\pi n^{3}} \left(\pi^{2} n^{2} \sin{\left (n \right )} - 2 n \cos{\left (n \right )} - \left(n^{2} - 2\right) \sin{\left (n \right )}\right)$$
Общее упрощение
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/     2\                         2  2       
\2 - n /*sin(n) - 2*n*cos(n) + pi *n *sin(n)
--------------------------------------------
                       3                    
                   pi*n                     
$$\frac{1}{\pi n^{3}} \left(\pi^{2} n^{2} \sin{\left (n \right )} - 2 n \cos{\left (n \right )} + \left(- n^{2} + 2\right) \sin{\left (n \right )}\right)$$
Собрать выражение
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             5             4             3       
pi*sin(n)   n *sin(n)   2*n *cos(n)   2*n *sin(n)
--------- - --------- - ----------- + -----------
    n           pi           pi            pi    
$$- \frac{n^{5}}{\pi} \sin{\left (n \right )} - \frac{2 n^{4}}{\pi} \cos{\left (n \right )} + \frac{2 n^{3}}{\pi} \sin{\left (n \right )} + \frac{\pi}{n} \sin{\left (n \right )}$$
Общий знаменатель
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            2                         2  2       
2*sin(n) - n *sin(n) - 2*n*cos(n) + pi *n *sin(n)
-------------------------------------------------
                          3                      
                      pi*n                       
$$\frac{1}{\pi n^{3}} \left(- n^{2} \sin{\left (n \right )} + \pi^{2} n^{2} \sin{\left (n \right )} - 2 n \cos{\left (n \right )} + 2 \sin{\left (n \right )}\right)$$
Тригонометрическая часть
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            / 2    \                    
pi*sin(n)   \n  - 2/*sin(n) + 2*n*cos(n)
--------- - ----------------------------
    n                      3            
                       pi*n             
$$\frac{\pi}{n} \sin{\left (n \right )} - \frac{1}{\pi n^{3}} \left(2 n \cos{\left (n \right )} + \left(n^{2} - 2\right) \sin{\left (n \right )}\right)$$
Комбинаторика
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            2                         2  2       
2*sin(n) - n *sin(n) - 2*n*cos(n) + pi *n *sin(n)
-------------------------------------------------
                          3                      
                      pi*n                       
$$\frac{1}{\pi n^{3}} \left(- n^{2} \sin{\left (n \right )} + \pi^{2} n^{2} \sin{\left (n \right )} - 2 n \cos{\left (n \right )} + 2 \sin{\left (n \right )}\right)$$
Раскрыть выражение
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            / 2    \                    
pi*sin(n)   \n  - 2/*sin(n) + 2*n*cos(n)
--------- - ----------------------------
    n                      3            
                       pi*n             
$$\frac{\pi}{n} \sin{\left (n \right )} - \frac{1}{\pi n^{3}} \left(2 n \cos{\left (n \right )} + \left(n^{2} - 2\right) \sin{\left (n \right )}\right)$$
             3 //      2\                    \
pi*sin(n)   n *\\-2 + n /*sin(n) + 2*n*cos(n)/
--------- - ----------------------------------
    n                       pi                
$$- \frac{n^{3}}{\pi} \left(2 n \cos{\left (n \right )} + \left(n^{2} - 2\right) \sin{\left (n \right )}\right) + \frac{\pi}{n} \sin{\left (n \right )}$$
Рациональный знаменатель
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  /  /      2\                    \     2  3       
n*\- \-2 + n /*sin(n) - 2*n*cos(n)/ + pi *n *sin(n)
---------------------------------------------------
                           4                       
                       pi*n                        
$$\frac{1}{\pi n^{4}} \left(\pi^{2} n^{3} \sin{\left (n \right )} + n \left(- 2 n \cos{\left (n \right )} - \left(n^{2} - 2\right) \sin{\left (n \right )}\right)\right)$$