Общий знаменатель (((4*x^2-2)*sin(2*x)+4*x* ... os(2*x)))/2+6*sin(2*x))/2

Вы ввели

/   2    \                                                                   
\4*x  - 2/*sin(2*x) + 4*x*cos(2*x)   5*(2*x*sin(2*x) + cos(2*x))             
---------------------------------- + --------------------------- + 6*sin(2*x)
                4                                 2                          
-----------------------------------------------------------------------------
                                      2                                      

$$\frac{1}{2} \left(\frac{5}{2} \left(2 x \sin{\left (2 x \right )} + \cos{\left (2 x \right )}\right) + \frac{1}{4} \left(4 x \cos{\left (2 x \right )} + \left(4 x^{2} - 2\right) \sin{\left (2 x \right )}\right) + 6 \sin{\left (2 x \right )}\right)$$

Степени

                                       /        2\                        
             5*cos(2*x)   x*cos(2*x)   \-2 + 4*x /*sin(2*x)   5*x*sin(2*x)
3*sin(2*x) + ---------- + ---------- + -------------------- + ------------
                 4            2                 8                  2      

$$\frac{5 x}{2} \sin{\left (2 x \right )} + \frac{x}{2} \cos{\left (2 x \right )} + \frac{1}{8} \left(4 x^{2} - 2\right) \sin{\left (2 x \right )} + 3 \sin{\left (2 x \right )} + \frac{5}{4} \cos{\left (2 x \right )}$$

Численный ответ

3.0*sin(2*x) + 1.25*cos(2*x) + 0.125*(-2.0 + 4.0*x^2)*sin(2*x) + 0.5*x*cos(2*x) + 2.5*x*sin(2*x)

Рациональный знаменатель

                                       /        2\                        
             5*cos(2*x)   x*cos(2*x)   \-2 + 4*x /*sin(2*x)   5*x*sin(2*x)
3*sin(2*x) + ---------- + ---------- + -------------------- + ------------
                 4            2                 8                  2      

$$\frac{5 x}{2} \sin{\left (2 x \right )} + \frac{x}{2} \cos{\left (2 x \right )} + \frac{1}{8} \left(4 x^{2} - 2\right) \sin{\left (2 x \right )} + 3 \sin{\left (2 x \right )} + \frac{5}{4} \cos{\left (2 x \right )}$$

Объединение рациональных выражений

                           /        2\                                        
5*cos(2*x) + 12*sin(2*x) + \-1 + 2*x /*sin(2*x) + 2*x*cos(2*x) + 10*x*sin(2*x)
------------------------------------------------------------------------------
                                      4                                       

$$\frac{1}{4} \left(10 x \sin{\left (2 x \right )} + 2 x \cos{\left (2 x \right )} + \left(2 x^{2} - 1\right) \sin{\left (2 x \right )} + 12 \sin{\left (2 x \right )} + 5 \cos{\left (2 x \right )}\right)$$

Общее упрощение

                                         2                        
5*cos(2*x)   11*sin(2*x)   x*cos(2*x)   x *sin(2*x)   5*x*sin(2*x)
---------- + ----------- + ---------- + ----------- + ------------
    4             4            2             2             2      

$$\frac{x^{2}}{2} \sin{\left (2 x \right )} + \frac{5 x}{2} \sin{\left (2 x \right )} + \frac{x}{2} \cos{\left (2 x \right )} + \frac{11}{4} \sin{\left (2 x \right )} + \frac{5}{4} \cos{\left (2 x \right )}$$

Собрать выражение

                                           /   2    \                        
             5*(2*x*sin(2*x) + cos(2*x))   \4*x  - 2/*sin(2*x) + 4*x*cos(2*x)
3*sin(2*x) + --------------------------- + ----------------------------------
                         2*2                              2*4                

$$\frac{5}{4} \left(2 x \sin{\left (2 x \right )} + \cos{\left (2 x \right )}\right) + \frac{1}{8} \left(4 x \cos{\left (2 x \right )} + \left(4 x^{2} - 2\right) \sin{\left (2 x \right )}\right) + 3 \sin{\left (2 x \right )}$$

                     /        2       \         
(5 + 2*x)*cos(2*x)   \11 + 2*x  + 10*x/*sin(2*x)
------------------ + ---------------------------
        4                         4             

$$\frac{1}{4} \left(2 x + 5\right) \cos{\left (2 x \right )} + \frac{1}{4} \left(2 x^{2} + 10 x + 11\right) \sin{\left (2 x \right )}$$

Комбинаторика

                                             2                         
5*cos(2*x) + 11*sin(2*x) + 2*x*cos(2*x) + 2*x *sin(2*x) + 10*x*sin(2*x)
-----------------------------------------------------------------------
                                   4                                   

$$\frac{1}{4} \left(2 x^{2} \sin{\left (2 x \right )} + 10 x \sin{\left (2 x \right )} + 2 x \cos{\left (2 x \right )} + 11 \sin{\left (2 x \right )} + 5 \cos{\left (2 x \right )}\right)$$

Общий знаменатель

                                         2                        
5*cos(2*x)   11*sin(2*x)   x*cos(2*x)   x *sin(2*x)   5*x*sin(2*x)
---------- + ----------- + ---------- + ----------- + ------------
    4             4            2             2             2      

$$\frac{x^{2}}{2} \sin{\left (2 x \right )} + \frac{5 x}{2} \sin{\left (2 x \right )} + \frac{x}{2} \cos{\left (2 x \right )} + \frac{11}{4} \sin{\left (2 x \right )} + \frac{5}{4} \cos{\left (2 x \right )}$$

Тригонометрическая часть

                                         2                        
5*cos(2*x)   11*sin(2*x)   x*cos(2*x)   x *sin(2*x)   5*x*sin(2*x)
---------- + ----------- + ---------- + ----------- + ------------
    4             4            2             2             2      

$$\frac{x^{2}}{2} \sin{\left (2 x \right )} + \frac{5 x}{2} \sin{\left (2 x \right )} + \frac{x}{2} \cos{\left (2 x \right )} + \frac{11}{4} \sin{\left (2 x \right )} + \frac{5}{4} \cos{\left (2 x \right )}$$

Раскрыть выражение

       2           2        /   2         2   \                                         /        2\              
  5*sin (x)   5*cos (x)   x*\cos (x) - sin (x)/                                         \-4 + 8*x /*cos(x)*sin(x)
- --------- + --------- + --------------------- + 6*cos(x)*sin(x) + 5*x*cos(x)*sin(x) + -------------------------
      4           4                 2                                                               8            

$$\frac{x}{2} \left(- \sin^{2}{\left (x \right )} + \cos^{2}{\left (x \right )}\right) + 5 x \sin{\left (x \right )} \cos{\left (x \right )} + \frac{1}{8} \left(8 x^{2} - 4\right) \sin{\left (x \right )} \cos{\left (x \right )} - \frac{5}{4} \sin^{2}{\left (x \right )} + 6 \sin{\left (x \right )} \cos{\left (x \right )} + \frac{5}{4} \cos^{2}{\left (x \right )}$$