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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)

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

Expresión a simplificar:

Solución

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