Общий знаменатель (((9*x^2-2)*sin(3*x)+6*x* ... cos(3*x))/9-4*sin(3*x))/3

Вы ввели

/   2    \                                     
\9*x  - 2/*sin(3*x) + 6*x*cos(3*x)             
---------------------------------- - 4*sin(3*x)
                9                              
-----------------------------------------------
                       3                       

$$\frac{1}{3} \left(\frac{1}{9} \left(6 x \cos{\left (3 x \right )} + \left(9 x^{2} - 2\right) \sin{\left (3 x \right )}\right) - 4 \sin{\left (3 x \right )}\right)$$

Степени

               /        2\                        
  4*sin(3*x)   \-2 + 9*x /*sin(3*x)   2*x*cos(3*x)
- ---------- + -------------------- + ------------
      3                 27                 9      

$$\frac{2 x}{9} \cos{\left (3 x \right )} + \frac{1}{27} \left(9 x^{2} - 2\right) \sin{\left (3 x \right )} - \frac{4}{3} \sin{\left (3 x \right )}$$

Численный ответ

-1.33333333333333*sin(3*x) + 0.037037037037037*(-2.0 + 9.0*x^2)*sin(3*x) + 0.222222222222222*x*cos(3*x)

Рациональный знаменатель

               /        2\                        
  4*sin(3*x)   \-2 + 9*x /*sin(3*x)   2*x*cos(3*x)
- ---------- + -------------------- + ------------
      3                 27                 9      

$$\frac{2 x}{9} \cos{\left (3 x \right )} + \frac{1}{27} \left(9 x^{2} - 2\right) \sin{\left (3 x \right )} - \frac{4}{3} \sin{\left (3 x \right )}$$

Объединение рациональных выражений

               /        2\                        
-36*sin(3*x) + \-2 + 9*x /*sin(3*x) + 6*x*cos(3*x)
--------------------------------------------------
                        27                        

$$\frac{1}{27} \left(6 x \cos{\left (3 x \right )} + \left(9 x^{2} - 2\right) \sin{\left (3 x \right )} - 36 \sin{\left (3 x \right )}\right)$$

Общее упрощение

                 2                        
  38*sin(3*x)   x *sin(3*x)   2*x*cos(3*x)
- ----------- + ----------- + ------------
       27            3             9      

$$\frac{x^{2}}{3} \sin{\left (3 x \right )} + \frac{2 x}{9} \cos{\left (3 x \right )} - \frac{38}{27} \sin{\left (3 x \right )}$$

Собрать выражение

/         2\                        
\-38 + 9*x /*sin(3*x)   2*x*cos(3*x)
--------------------- + ------------
          27                 9      

$$\frac{2 x}{9} \cos{\left (3 x \right )} + \frac{1}{27} \left(9 x^{2} - 38\right) \sin{\left (3 x \right )}$$

               /   2    \                        
  4*sin(3*x)   \9*x  - 2/*sin(3*x) + 6*x*cos(3*x)
- ---------- + ----------------------------------
      3                       3*9                

$$\frac{1}{27} \left(6 x \cos{\left (3 x \right )} + \left(9 x^{2} - 2\right) \sin{\left (3 x \right )}\right) - \frac{4}{3} \sin{\left (3 x \right )}$$

Комбинаторика

                                 2         
-38*sin(3*x) + 6*x*cos(3*x) + 9*x *sin(3*x)
-------------------------------------------
                     27                    

$$\frac{1}{27} \left(9 x^{2} \sin{\left (3 x \right )} + 6 x \cos{\left (3 x \right )} - 38 \sin{\left (3 x \right )}\right)$$

Общий знаменатель

                 2                        
  38*sin(3*x)   x *sin(3*x)   2*x*cos(3*x)
- ----------- + ----------- + ------------
       27            3             9      

$$\frac{x^{2}}{3} \sin{\left (3 x \right )} + \frac{2 x}{9} \cos{\left (3 x \right )} - \frac{38}{27} \sin{\left (3 x \right )}$$

Тригонометрическая часть

                 2                        
  38*sin(3*x)   x *sin(3*x)   2*x*cos(3*x)
- ----------- + ----------- + ------------
       27            3             9      

$$\frac{x^{2}}{3} \sin{\left (3 x \right )} + \frac{2 x}{9} \cos{\left (3 x \right )} - \frac{38}{27} \sin{\left (3 x \right )}$$

Раскрыть выражение

     3                         /        2\ /     3           2          \       /   3           2          \
4*sin (x)        2             \-2 + 9*x /*\- sin (x) + 3*cos (x)*sin(x)/   2*x*\cos (x) - 3*sin (x)*cos(x)/
--------- - 4*cos (x)*sin(x) + ------------------------------------------ + --------------------------------
    3                                              27                                      9                

$$\frac{2 x}{9} \left(- 3 \sin^{2}{\left (x \right )} \cos{\left (x \right )} + \cos^{3}{\left (x \right )}\right) + \frac{1}{27} \left(9 x^{2} - 2\right) \left(- \sin^{3}{\left (x \right )} + 3 \sin{\left (x \right )} \cos^{2}{\left (x \right )}\right) + \frac{4}{3} \sin^{3}{\left (x \right )} - 4 \sin{\left (x \right )} \cos^{2}{\left (x \right )}$$