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Simplificación de expresiones/ Descomposición en fracciones simples/ atan(x/2)/16+x/(8*(4+x^2))

¿Cómo vas a descomponer esta atan(x/2)/16+x/(8*(4+x^2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /x\             
atan|-|             
    \2/       x     
------- + ----------
   16       /     2\
          8*\4 + x /
$$\frac{x}{8 \left(x^{2} + 4\right)} + \frac{\operatorname{atan}{\left(\frac{x}{2} \right)}}{16}$$ 
atan(x/2)/16 + x/((8*(4 + x^2)))
Simplificación general [src] 
      /     2\     /x\
2*x + \4 + x /*atan|-|
                   \2/
----------------------
        /     2\      
     16*\4 + x /
$$\frac{2 x + \left(x^{2} + 4\right) \operatorname{atan}{\left(\frac{x}{2} \right)}}{16 \left(x^{2} + 4\right)}$$ 
(2*x + (4 + x^2)*atan(x/2))/(16*(4 + x^2))
Respuesta numérica [src] 
0.0625*atan(x/2) + x/(32.0 + 8.0*x^2)
0.0625*atan(x/2) + x/(32.0 + 8.0*x^2)
Parte trigonométrica [src] 
    /x\            
atan|-|            
    \2/       x    
------- + ---------
   16             2
          32 + 8*x
$$\frac{x}{8 x^{2} + 32} + \frac{\operatorname{atan}{\left(\frac{x}{2} \right)}}{16}$$ 
atan(x/2)/16 + x/(32 + 8*x^2)
Potencias [src] 
    /x\            
atan|-|            
    \2/       x    
------- + ---------
   16             2
          32 + 8*x
$$\frac{x}{8 x^{2} + 32} + \frac{\operatorname{atan}{\left(\frac{x}{2} \right)}}{16}$$ 
atan(x/2)/16 + x/(32 + 8*x^2)
Denominador común [src] 
    /x\            
atan|-|            
    \2/       x    
------- + ---------
   16             2
          32 + 8*x
$$\frac{x}{8 x^{2} + 32} + \frac{\operatorname{atan}{\left(\frac{x}{2} \right)}}{16}$$ 
atan(x/2)/16 + x/(32 + 8*x^2)
Unión de expresiones racionales [src] 
      /     2\     /x\
2*x + \4 + x /*atan|-|
                   \2/
----------------------
        /     2\      
     16*\4 + x /
$$\frac{2 x + \left(x^{2} + 4\right) \operatorname{atan}{\left(\frac{x}{2} \right)}}{16 \left(x^{2} + 4\right)}$$ 
(2*x + (4 + x^2)*atan(x/2))/(16*(4 + x^2))
Denominador racional [src] 
       /        2\     /x\
16*x + \32 + 8*x /*atan|-|
                       \2/
--------------------------
                  2       
       512 + 128*x
$$\frac{16 x + \left(8 x^{2} + 32\right) \operatorname{atan}{\left(\frac{x}{2} \right)}}{128 x^{2} + 512}$$ 
(16*x + (32 + 8*x^2)*atan(x/2))/(512 + 128*x^2)
Compilar la expresión [src] 
    /x\            
atan|-|            
    \2/       x    
------- + ---------
   16             2
          32 + 8*x
$$\frac{x}{8 x^{2} + 32} + \frac{\operatorname{atan}{\left(\frac{x}{2} \right)}}{16}$$ 
atan(x/2)/16 + x/(32 + 8*x^2)
Combinatoria [src] 
            /x\    2     /x\
2*x + 4*atan|-| + x *atan|-|
            \2/          \2/
----------------------------
           /     2\         
        16*\4 + x /
$$\frac{x^{2} \operatorname{atan}{\left(\frac{x}{2} \right)} + 2 x + 4 \operatorname{atan}{\left(\frac{x}{2} \right)}}{16 \left(x^{2} + 4\right)}$$ 
(2*x + 4*atan(x/2) + x^2*atan(x/2))/(16*(4 + x^2))
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