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Simplificación de expresiones/ Descomposición en fracciones simples/ atan(5*x)/(x^3)-5/(2*x^2*(25*x^2+1))-125/(2+50*x^2)-5/(2*x)

¿Cómo vas a descomponer esta atan(5*x)/(x^3)-5/(2*x^2*(25*x^2+1))-125/(2+50*x^2)-5/(2*x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
atan(5*x)          5              125       5 
--------- - ---------------- - --------- - ---
     3         2 /    2    \           2   2*x
    x       2*x *\25*x  + 1/   2 + 50*x
$$\left(\left(- \frac{5}{2 x^{2} \left(25 x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(5 x \right)}}{x^{3}}\right) - \frac{125}{50 x^{2} + 2}\right) - \frac{5}{2 x}$$ 
atan(5*x)/x^3 - 5*1/(2*x^2*(25*x^2 + 1)) - 125/(2 + 50*x^2) - 5*1/(2*x)
Simplificación general [src] 
           2            
  5*x   5*x             
- --- - ---- + atan(5*x)
   2     2              
------------------------
            3           
           x
$$\frac{- \frac{5 x^{2}}{2} - \frac{5 x}{2} + \operatorname{atan}{\left(5 x \right)}}{x^{3}}$$ 
(-5*x/2 - 5*x^2/2 + atan(5*x))/x^3
Respuesta numérica [src] 
-2.5/x - 125.0/(2.0 + 50.0*x^2) + atan(5*x)/x^3 - 2.5/(x^2*(1.0 + 25.0*x^2))
-2.5/x - 125.0/(2.0 + 50.0*x^2) + atan(5*x)/x^3 - 2.5/(x^2*(1.0 + 25.0*x^2))
Compilar la expresión [src] 
     125       5    atan(5*x)          5        
- --------- - --- + --------- - ----------------
          2   2*x        3         2 /        2\
  2 + 50*x              x       2*x *\1 + 25*x /
$$- \frac{125}{50 x^{2} + 2} - \frac{5}{2 x} - \frac{5}{2 x^{2} \left(25 x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(5 x \right)}}{x^{3}}$$ 
-125/(2 + 50*x^2) - 5/(2*x) + atan(5*x)/x^3 - 5/(2*x^2*(1 + 25*x^2))
Abrimos la expresión [src] 
     125       5    atan(5*x)          5        
- --------- - --- + --------- - ----------------
          2   2*x        3         2 /    2    \
  2 + 50*x              x       2*x *\25*x  + 1/
$$- \frac{125}{50 x^{2} + 2} + \frac{\operatorname{atan}{\left(5 x \right)}}{x^{3}} - \frac{5}{2 x} - \frac{5}{2 x^{2} \left(25 x^{2} + 1\right)}$$ 
-125/(2 + 50*x^2) - 5/(2*x) + atan(5*x)/x^3 - 5/(2*x^2*(25*x^2 + 1))
Denominador común [src] 
 /                        2\ 
-\-2*atan(5*x) + 5*x + 5*x / 
-----------------------------
                3            
             2*x
$$- \frac{5 x^{2} + 5 x - 2 \operatorname{atan}{\left(5 x \right)}}{2 x^{3}}$$ 
-(-2*atan(5*x) + 5*x + 5*x^2)/(2*x^3)
Combinatoria [src] 
 /                        2\ 
-\-2*atan(5*x) + 5*x + 5*x / 
-----------------------------
                3            
             2*x
$$- \frac{5 x^{2} + 5 x - 2 \operatorname{atan}{\left(5 x \right)}}{2 x^{3}}$$ 
-(-2*atan(5*x) + 5*x + 5*x^2)/(2*x^3)
Potencias [src] 
     125       5    atan(5*x)          5        
- --------- - --- + --------- - ----------------
          2   2*x        3         2 /        2\
  2 + 50*x              x       2*x *\1 + 25*x /
$$- \frac{125}{50 x^{2} + 2} - \frac{5}{2 x} - \frac{5}{2 x^{2} \left(25 x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(5 x \right)}}{x^{3}}$$ 
     125       5    atan(5*x)         5       
- --------- - --- + --------- - --------------
          2   2*x        3       2 /        2\
  2 + 50*x              x       x *\2 + 50*x /
$$- \frac{125}{50 x^{2} + 2} - \frac{5}{2 x} - \frac{5}{x^{2} \left(50 x^{2} + 2\right)} + \frac{\operatorname{atan}{\left(5 x \right)}}{x^{3}}$$ 
-125/(2 + 50*x^2) - 5/(2*x) + atan(5*x)/x^3 - 5/(x^2*(2 + 50*x^2))
Unión de expresiones racionales [src] 
       3            2 /        2\     /        2\          
- 125*x  - 5*x - 5*x *\1 + 25*x / + 2*\1 + 25*x /*atan(5*x)
-----------------------------------------------------------
                         3 /        2\                     
                      2*x *\1 + 25*x /
$$\frac{- 125 x^{3} - 5 x^{2} \left(25 x^{2} + 1\right) - 5 x + 2 \left(25 x^{2} + 1\right) \operatorname{atan}{\left(5 x \right)}}{2 x^{3} \left(25 x^{2} + 1\right)}$$ 
(-125*x^3 - 5*x - 5*x^2*(1 + 25*x^2) + 2*(1 + 25*x^2)*atan(5*x))/(2*x^3*(1 + 25*x^2))
Parte trigonométrica [src] 
     125       5    atan(5*x)          5        
- --------- - --- + --------- - ----------------
          2   2*x        3         2 /        2\
  2 + 50*x              x       2*x *\1 + 25*x /
$$- \frac{125}{50 x^{2} + 2} - \frac{5}{2 x} - \frac{5}{2 x^{2} \left(25 x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(5 x \right)}}{x^{3}}$$ 
-125/(2 + 50*x^2) - 5/(2*x) + atan(5*x)/x^3 - 5/(2*x^2*(1 + 25*x^2))
Denominador racional [src] 
    //        2\ /     3      2 /        2\          \        5 /        2\\       5 /        2\ /        2\
2*x*\\2 + 50*x /*\- 5*x  + 2*x *\1 + 25*x /*atan(5*x)/ - 250*x *\1 + 25*x // - 10*x *\1 + 25*x /*\2 + 50*x /
------------------------------------------------------------------------------------------------------------
                                           6 /        2\ /        2\                                        
                                        4*x *\1 + 25*x /*\2 + 50*x /
$$\frac{- 10 x^{5} \left(25 x^{2} + 1\right) \left(50 x^{2} + 2\right) + 2 x \left(- 250 x^{5} \left(25 x^{2} + 1\right) + \left(50 x^{2} + 2\right) \left(- 5 x^{3} + 2 x^{2} \left(25 x^{2} + 1\right) \operatorname{atan}{\left(5 x \right)}\right)\right)}{4 x^{6} \left(25 x^{2} + 1\right) \left(50 x^{2} + 2\right)}$$ 
(2*x*((2 + 50*x^2)*(-5*x^3 + 2*x^2*(1 + 25*x^2)*atan(5*x)) - 250*x^5*(1 + 25*x^2)) - 10*x^5*(1 + 25*x^2)*(2 + 50*x^2))/(4*x^6*(1 + 25*x^2)*(2 + 50*x^2))
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