Sr Examen

Otras calculadoras

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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    /  x  \           
atan|-----|           
    |  ___|           
    \\/ 2 /      x    
----------- - --------
     3/2             2
    2         4 + 2*x
−x2x2+4+atan⁡(x2)232- \frac{x}{2 x^{2} + 4} + \frac{\operatorname{atan}{\left(\frac{x}{\sqrt{2}} \right)}}{2^{\frac{3}{2}}} 
atan(x/sqrt(2))/2^(3/2) - x/(4 + 2*x^2)
Simplificación general [src] 
                          /    ___\
         ___ /     2\     |x*\/ 2 |
-2*x + \/ 2 *\2 + x /*atan|-------|
                          \   2   /
-----------------------------------
               /     2\            
             4*\2 + x /
−2x+2(x2+2)atan⁡(2x2)4(x2+2)\frac{- 2 x + \sqrt{2} \left(x^{2} + 2\right) \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4 \left(x^{2} + 2\right)} 
(-2*x + sqrt(2)*(2 + x^2)*atan(x*sqrt(2)/2))/(4*(2 + x^2))
Respuesta numérica [src] 
0.353553390593274*atan(x/sqrt(2)) - x/(4.0 + 2.0*x^2)
0.353553390593274*atan(x/sqrt(2)) - x/(4.0 + 2.0*x^2)
Potencias [src] 
                       /    ___\
               ___     |x*\/ 2 |
             \/ 2 *atan|-------|
     x                 \   2   /
- -------- + -------------------
         2            4         
  4 + 2*x
−x2x2+4+2atan⁡(2x2)4- \frac{x}{2 x^{2} + 4} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4} 
-x/(4 + 2*x^2) + sqrt(2)*atan(x*sqrt(2)/2)/4
Compilar la expresión [src] 
               ___     /  x  \
             \/ 2 *atan|-----|
                       |  ___|
     x                 \\/ 2 /
- -------- + -----------------
         2           4        
  4 + 2*x
−x2x2+4+2atan⁡(x2)4- \frac{x}{2 x^{2} + 4} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{x}{\sqrt{2}} \right)}}{4} 
-x/(4 + 2*x^2) + sqrt(2)*atan(x/sqrt(2))/4
Parte trigonométrica [src] 
                       /    ___\
               ___     |x*\/ 2 |
             \/ 2 *atan|-------|
     x                 \   2   /
- -------- + -------------------
         2            4         
  4 + 2*x
−x2x2+4+2atan⁡(2x2)4- \frac{x}{2 x^{2} + 4} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4} 
-x/(4 + 2*x^2) + sqrt(2)*atan(x*sqrt(2)/2)/4
Denominador racional [src] 
                   /    ___\                /    ___\
           ___     |x*\/ 2 |     ___  2     |x*\/ 2 |
-2*x + 2*\/ 2 *atan|-------| + \/ 2 *x *atan|-------|
                   \   2   /                \   2   /
-----------------------------------------------------
                              2                      
                       8 + 4*x
2x2atan⁡(2x2)−2x+22atan⁡(2x2)4x2+8\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)}}{4 x^{2} + 8} 
(-2*x + 2*sqrt(2)*atan(x*sqrt(2)/2) + sqrt(2)*x^2*atan(x*sqrt(2)/2))/(8 + 4*x^2)
Denominador común [src] 
                       /    ___\
               ___     |x*\/ 2 |
             \/ 2 *atan|-------|
     x                 \   2   /
- -------- + -------------------
         2            4         
  4 + 2*x
−x2x2+4+2atan⁡(2x2)4- \frac{x}{2 x^{2} + 4} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4} 
-x/(4 + 2*x^2) + sqrt(2)*atan(x*sqrt(2)/2)/4
Combinatoria [src] 
                   /    ___\                /    ___\
           ___     |x*\/ 2 |     ___  2     |x*\/ 2 |
-2*x + 2*\/ 2 *atan|-------| + \/ 2 *x *atan|-------|
                   \   2   /                \   2   /
-----------------------------------------------------
                        /     2\                     
                      4*\2 + x /
2x2atan⁡(2x2)−2x+22atan⁡(2x2)4(x2+2)\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)}}{4 \left(x^{2} + 2\right)} 
(-2*x + 2*sqrt(2)*atan(x*sqrt(2)/2) + sqrt(2)*x^2*atan(x*sqrt(2)/2))/(4*(2 + x^2))
Unión de expresiones racionales [src] 
                          /    ___\
         ___ /     2\     |x*\/ 2 |
-2*x + \/ 2 *\2 + x /*atan|-------|
                          \   2   /
-----------------------------------
               /     2\            
             4*\2 + x /
−2x+2(x2+2)atan⁡(2x2)4(x2+2)\frac{- 2 x + \sqrt{2} \left(x^{2} + 2\right) \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4 \left(x^{2} + 2\right)} 
(-2*x + sqrt(2)*(2 + x^2)*atan(x*sqrt(2)/2))/(4*(2 + x^2))
    © Sr Examen – Калькулятор