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Simplificación de expresiones/ Descomposición en fracciones simples/ atan(x/sqrt(2))/2^(5/2)+x/(8+4*x^2)

¿Cómo vas a descomponer esta atan(x/sqrt(2))/2^(5/2)+x/(8+4*x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /  x  \           
atan|-----|           
    |  ___|           
    \\/ 2 /      x    
----------- + --------
     5/2             2
    2         8 + 4*x
$$\frac{x}{4 x^{2} + 8} + \frac{\operatorname{atan}{\left(\frac{x}{\sqrt{2}} \right)}}{2^{\frac{5}{2}}}$$ 
atan(x/sqrt(2))/2^(5/2) + x/(8 + 4*x^2)
Simplificación general [src] 
                         /    ___\
        ___ /     2\     |x*\/ 2 |
2*x + \/ 2 *\2 + x /*atan|-------|
                         \   2   /
----------------------------------
              /     2\            
            8*\2 + x /
$$\frac{2 x + \sqrt{2} \left(x^{2} + 2\right) \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{8 \left(x^{2} + 2\right)}$$ 
(2*x + sqrt(2)*(2 + x^2)*atan(x*sqrt(2)/2))/(8*(2 + x^2))
Respuesta numérica [src] 
0.176776695296637*atan(x/sqrt(2)) + x/(8.0 + 4.0*x^2)
0.176776695296637*atan(x/sqrt(2)) + x/(8.0 + 4.0*x^2)
Potencias [src] 
                     /    ___\
             ___     |x*\/ 2 |
           \/ 2 *atan|-------|
   x                 \   2   /
-------- + -------------------
       2            8         
8 + 4*x
$$\frac{x}{4 x^{2} + 8} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{8}$$ 
x/(8 + 4*x^2) + sqrt(2)*atan(x*sqrt(2)/2)/8
Denominador racional [src] 
                  /    ___\                /    ___\
          ___     |x*\/ 2 |     ___  2     |x*\/ 2 |
2*x + 2*\/ 2 *atan|-------| + \/ 2 *x *atan|-------|
                  \   2   /                \   2   /
----------------------------------------------------
                             2                      
                     16 + 8*x
$$\frac{\sqrt{2} x^{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} + 2 x + 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{8 x^{2} + 16}$$ 
(2*x + 2*sqrt(2)*atan(x*sqrt(2)/2) + sqrt(2)*x^2*atan(x*sqrt(2)/2))/(16 + 8*x^2)
Unión de expresiones racionales [src] 
                         /    ___\
        ___ /     2\     |x*\/ 2 |
2*x + \/ 2 *\2 + x /*atan|-------|
                         \   2   /
----------------------------------
              /     2\            
            8*\2 + x /
$$\frac{2 x + \sqrt{2} \left(x^{2} + 2\right) \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{8 \left(x^{2} + 2\right)}$$ 
(2*x + sqrt(2)*(2 + x^2)*atan(x*sqrt(2)/2))/(8*(2 + x^2))
Denominador común [src] 
                     /    ___\
             ___     |x*\/ 2 |
           \/ 2 *atan|-------|
   x                 \   2   /
-------- + -------------------
       2            8         
8 + 4*x
$$\frac{x}{4 x^{2} + 8} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{8}$$ 
x/(8 + 4*x^2) + sqrt(2)*atan(x*sqrt(2)/2)/8
Parte trigonométrica [src] 
                     /    ___\
             ___     |x*\/ 2 |
           \/ 2 *atan|-------|
   x                 \   2   /
-------- + -------------------
       2            8         
8 + 4*x
$$\frac{x}{4 x^{2} + 8} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{8}$$ 
x/(8 + 4*x^2) + sqrt(2)*atan(x*sqrt(2)/2)/8
Compilar la expresión [src] 
             ___     /  x  \
           \/ 2 *atan|-----|
                     |  ___|
   x                 \\/ 2 /
-------- + -----------------
       2           8        
8 + 4*x
$$\frac{x}{4 x^{2} + 8} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{x}{\sqrt{2}} \right)}}{8}$$ 
x/(8 + 4*x^2) + sqrt(2)*atan(x/sqrt(2))/8
Combinatoria [src] 
                  /    ___\                /    ___\
          ___     |x*\/ 2 |     ___  2     |x*\/ 2 |
2*x + 2*\/ 2 *atan|-------| + \/ 2 *x *atan|-------|
                  \   2   /                \   2   /
----------------------------------------------------
                       /     2\                     
                     8*\2 + x /
$$\frac{\sqrt{2} x^{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} + 2 x + 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{8 \left(x^{2} + 2\right)}$$ 
(2*x + 2*sqrt(2)*atan(x*sqrt(2)/2) + sqrt(2)*x^2*atan(x*sqrt(2)/2))/(8*(2 + x^2))
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