Общий знаменатель (2*((10*x*sin(5*x)+(2-25* ... (5*x)-5*x*cos(5*x))/5))/5

Вы ввели

  /                /        2\                                   \
  |10*x*sin(5*x) + \2 - 25*x /*cos(5*x)   sin(5*x) - 5*x*cos(5*x)|
2*|------------------------------------ - -----------------------|
  \                 25                               5           /
------------------------------------------------------------------
                                5                                 

$$\frac{2}{5} \left(- - x \cos{\left (5 x \right )} + \frac{1}{5} \sin{\left (5 x \right )} + \frac{1}{25} \left(10 x \sin{\left (5 x \right )} + \left(- 25 x^{2} + 2\right) \cos{\left (5 x \right )}\right)\right)$$

Степени

                                /        2\                        
  2*sin(5*x)   2*x*cos(5*x)   2*\2 - 25*x /*cos(5*x)   4*x*sin(5*x)
- ---------- + ------------ + ---------------------- + ------------
      25            5                  125                  25     

$$\frac{4 x}{25} \sin{\left (5 x \right )} + \frac{2 x}{5} \cos{\left (5 x \right )} + \frac{2}{125} \left(- 25 x^{2} + 2\right) \cos{\left (5 x \right )} - \frac{2}{25} \sin{\left (5 x \right )}$$

Численный ответ

-0.08*sin(5*x) + 0.016*(2.0 - 25.0*x^2)*cos(5*x) + 0.16*x*sin(5*x) + 0.4*x*cos(5*x)

Рациональный знаменатель

                                /        2\                        
  2*sin(5*x)   2*x*cos(5*x)   2*\2 - 25*x /*cos(5*x)   4*x*sin(5*x)
- ---------- + ------------ + ---------------------- + ------------
      25            5                  125                  25     

$$\frac{4 x}{25} \sin{\left (5 x \right )} + \frac{2 x}{5} \cos{\left (5 x \right )} + \frac{2}{125} \left(- 25 x^{2} + 2\right) \cos{\left (5 x \right )} - \frac{2}{25} \sin{\left (5 x \right )}$$

Объединение рациональных выражений

  /              /        2\                                         \
2*\-5*sin(5*x) + \2 - 25*x /*cos(5*x) + 10*x*sin(5*x) + 25*x*cos(5*x)/
----------------------------------------------------------------------
                                 125                                  

$$\frac{1}{125} \left(20 x \sin{\left (5 x \right )} + 50 x \cos{\left (5 x \right )} + 2 \left(- 25 x^{2} + 2\right) \cos{\left (5 x \right )} - 10 \sin{\left (5 x \right )}\right)$$

Общее упрощение

                                /        2\                        
  2*sin(5*x)   2*x*cos(5*x)   2*\2 - 25*x /*cos(5*x)   4*x*sin(5*x)
- ---------- + ------------ + ---------------------- + ------------
      25            5                  125                  25     

$$\frac{4 x}{25} \sin{\left (5 x \right )} + \frac{2 x}{5} \cos{\left (5 x \right )} + \frac{2}{125} \left(- 25 x^{2} + 2\right) \cos{\left (5 x \right )} - \frac{2}{25} \sin{\left (5 x \right )}$$

Собрать выражение

                        /        2       \         
(-10 + 20*x)*sin(5*x)   \4 - 50*x  + 50*x/*cos(5*x)
--------------------- + ---------------------------
         125                        125            

$$\frac{1}{125} \left(20 x - 10\right) \sin{\left (5 x \right )} + \frac{1}{125} \left(- 50 x^{2} + 50 x + 4\right) \cos{\left (5 x \right )}$$

                                  /                /        2\         \
  2*(sin(5*x) - 5*x*cos(5*x))   2*\10*x*sin(5*x) + \2 - 25*x /*cos(5*x)/
- --------------------------- + ----------------------------------------
              5*5                                 5*25                  

$$- - \frac{2 x}{5} \cos{\left (5 x \right )} + \frac{2}{25} \sin{\left (5 x \right )} + \frac{1}{125} \left(2 \cdot 10 x \sin{\left (5 x \right )} + 2 \left(- 25 x^{2} + 2\right) \cos{\left (5 x \right )}\right)$$

Комбинаторика

   /                                                               2         \
-2*\-2*cos(5*x) + 5*sin(5*x) - 25*x*cos(5*x) - 10*x*sin(5*x) + 25*x *cos(5*x)/
------------------------------------------------------------------------------
                                     125                                      

$$- \frac{1}{125} \left(50 x^{2} \cos{\left (5 x \right )} - 20 x \sin{\left (5 x \right )} - 50 x \cos{\left (5 x \right )} + 10 \sin{\left (5 x \right )} - 4 \cos{\left (5 x \right )}\right)$$

Общий знаменатель

                               2                                       
  2*sin(5*x)   4*cos(5*x)   2*x *cos(5*x)   2*x*cos(5*x)   4*x*sin(5*x)
- ---------- + ---------- - ------------- + ------------ + ------------
      25          125             5              5              25     

$$- \frac{2 x^{2}}{5} \cos{\left (5 x \right )} + \frac{4 x}{25} \sin{\left (5 x \right )} + \frac{2 x}{5} \cos{\left (5 x \right )} - \frac{2}{25} \sin{\left (5 x \right )} + \frac{4}{125} \cos{\left (5 x \right )}$$

Тригонометрическая часть

                                /        2\                        
  2*sin(5*x)   2*x*cos(5*x)   2*\2 - 25*x /*cos(5*x)   4*x*sin(5*x)
- ---------- + ------------ + ---------------------- + ------------
      25            5                  125                  25     

$$\frac{4 x}{25} \sin{\left (5 x \right )} + \frac{2 x}{5} \cos{\left (5 x \right )} + \frac{2}{125} \left(- 25 x^{2} + 2\right) \cos{\left (5 x \right )} - \frac{2}{25} \sin{\left (5 x \right )}$$

Раскрыть выражение

       5           4                 /   5            3       2           4          \     /        2\ /   5            3       2           4          \        2       3          /   5            2       3           4          \
  2*sin (x)   2*cos (x)*sin(x)   2*x*\cos (x) - 10*cos (x)*sin (x) + 5*sin (x)*cos(x)/   2*\2 - 25*x /*\cos (x) - 10*cos (x)*sin (x) + 5*sin (x)*cos(x)/   4*cos (x)*sin (x)   4*x*\sin (x) - 10*cos (x)*sin (x) + 5*cos (x)*sin(x)/
- --------- - ---------------- + ----------------------------------------------------- + --------------------------------------------------------------- + ----------------- + -----------------------------------------------------
      25             5                                     5                                                           125                                         5                                     25                         

$$\frac{2 x}{5} \left(5 \sin^{4}{\left (x \right )} \cos{\left (x \right )} - 10 \sin^{2}{\left (x \right )} \cos^{3}{\left (x \right )} + \cos^{5}{\left (x \right )}\right) + \frac{4 x}{25} \left(\sin^{5}{\left (x \right )} - 10 \sin^{3}{\left (x \right )} \cos^{2}{\left (x \right )} + 5 \sin{\left (x \right )} \cos^{4}{\left (x \right )}\right) + \frac{2}{125} \left(- 25 x^{2} + 2\right) \left(5 \sin^{4}{\left (x \right )} \cos{\left (x \right )} - 10 \sin^{2}{\left (x \right )} \cos^{3}{\left (x \right )} + \cos^{5}{\left (x \right )}\right) - \frac{2}{25} \sin^{5}{\left (x \right )} + \frac{4}{5} \sin^{3}{\left (x \right )} \cos^{2}{\left (x \right )} - \frac{2}{5} \sin{\left (x \right )} \cos^{4}{\left (x \right )}$$