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Simplificación de expresiones/ Descomposición en fracciones simples/ atan(x)/8+(x^3-x)/(8+16*x^2+8*x^4)

¿Cómo vas a descomponer esta atan(x)/8+(x^3-x)/(8+16*x^2+8*x^4) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                3         
atan(x)        x  - x     
------- + ----------------
   8              2      4
          8 + 16*x  + 8*x
x3−x8x4+(16x2+8)+atan⁡(x)8\frac{x^{3} - x}{8 x^{4} + \left(16 x^{2} + 8\right)} + \frac{\operatorname{atan}{\left(x \right)}}{8} 
atan(x)/8 + (x^3 - x)/(8 + 16*x^2 + 8*x^4)
Simplificación general [src] 
 3       /     4      2\        
x  - x + \1 + x  + 2*x /*atan(x)
--------------------------------
         /     4      2\        
       8*\1 + x  + 2*x /
x3−x+(x4+2x2+1)atan⁡(x)8(x4+2x2+1)\frac{x^{3} - x + \left(x^{4} + 2 x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}{8 \left(x^{4} + 2 x^{2} + 1\right)} 
(x^3 - x + (1 + x^4 + 2*x^2)*atan(x))/(8*(1 + x^4 + 2*x^2))
Respuesta numérica [src] 
0.125*atan(x) + (x^3 - x)/(8.0 + 8.0*x^4 + 16.0*x^2)
0.125*atan(x) + (x^3 - x)/(8.0 + 8.0*x^4 + 16.0*x^2)
Compilar la expresión [src] 
                3         
atan(x)        x  - x     
------- + ----------------
   8             4       2
          8 + 8*x  + 16*x
x3−x8x4+16x2+8+atan⁡(x)8\frac{x^{3} - x}{8 x^{4} + 16 x^{2} + 8} + \frac{\operatorname{atan}{\left(x \right)}}{8} 
atan(x)/8 + (x^3 - x)/(8 + 8*x^4 + 16*x^2)
Combinatoria [src] 
 3        4              2                  
x  - x + x *atan(x) + 2*x *atan(x) + atan(x)
--------------------------------------------
                          2                 
                  /     2\                  
                8*\1 + x /
x4atan⁡(x)+x3+2x2atan⁡(x)−x+atan⁡(x)8(x2+1)2\frac{x^{4} \operatorname{atan}{\left(x \right)} + x^{3} + 2 x^{2} \operatorname{atan}{\left(x \right)} - x + \operatorname{atan}{\left(x \right)}}{8 \left(x^{2} + 1\right)^{2}} 
(x^3 - x + x^4*atan(x) + 2*x^2*atan(x) + atan(x))/(8*(1 + x^2)^2)
Denominador común [src] 
                3         
atan(x)        x  - x     
------- + ----------------
   8             4       2
          8 + 8*x  + 16*x
x3−x8x4+16x2+8+atan⁡(x)8\frac{x^{3} - x}{8 x^{4} + 16 x^{2} + 8} + \frac{\operatorname{atan}{\left(x \right)}}{8} 
atan(x)/8 + (x^3 - x)/(8 + 8*x^4 + 16*x^2)
Parte trigonométrica [src] 
                3         
atan(x)        x  - x     
------- + ----------------
   8             4       2
          8 + 8*x  + 16*x
x3−x8x4+16x2+8+atan⁡(x)8\frac{x^{3} - x}{8 x^{4} + 16 x^{2} + 8} + \frac{\operatorname{atan}{\left(x \right)}}{8} 
atan(x)/8 + (x^3 - x)/(8 + 8*x^4 + 16*x^2)
Denominador racional [src] 
          3   /       4       2\        
-8*x + 8*x  + \8 + 8*x  + 16*x /*atan(x)
----------------------------------------
                   4        2           
          64 + 64*x  + 128*x
8x3−8x+(8x4+16x2+8)atan⁡(x)64x4+128x2+64\frac{8 x^{3} - 8 x + \left(8 x^{4} + 16 x^{2} + 8\right) \operatorname{atan}{\left(x \right)}}{64 x^{4} + 128 x^{2} + 64} 
(-8*x + 8*x^3 + (8 + 8*x^4 + 16*x^2)*atan(x))/(64 + 64*x^4 + 128*x^2)
Potencias [src] 
                3         
atan(x)        x  - x     
------- + ----------------
   8             4       2
          8 + 8*x  + 16*x
x3−x8x4+16x2+8+atan⁡(x)8\frac{x^{3} - x}{8 x^{4} + 16 x^{2} + 8} + \frac{\operatorname{atan}{\left(x \right)}}{8} 
atan(x)/8 + (x^3 - x)/(8 + 8*x^4 + 16*x^2)
Unión de expresiones racionales [src] 
  /      2\   /     4      2\        
x*\-1 + x / + \1 + x  + 2*x /*atan(x)
-------------------------------------
            /     4      2\          
          8*\1 + x  + 2*x /
x(x2−1)+(x4+2x2+1)atan⁡(x)8(x4+2x2+1)\frac{x \left(x^{2} - 1\right) + \left(x^{4} + 2 x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}{8 \left(x^{4} + 2 x^{2} + 1\right)} 
(x*(-1 + x^2) + (1 + x^4 + 2*x^2)*atan(x))/(8*(1 + x^4 + 2*x^2))
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