Sr Examen
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?
Solución
Ha introducido
[src]
/ x \
atan|-----|
| ___|
\\/ 2 / x
----------- - --------
3/2 2
2 4 + 2*x
$$- \frac{x}{2 x^{2} + 4} + \frac{\operatorname{atan}{\left(\frac{x}{\sqrt{2}} \right)}}{2^{\frac{3}{2}}}$$
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 /
$$\frac{- 2 x + \sqrt{2} \left(x^{2} + 2\right) \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4 \left(x^{2} + 2\right)}$$
(-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
$$- \frac{x}{2 x^{2} + 4} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4}$$
-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
$$- \frac{x}{2 x^{2} + 4} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{x}{\sqrt{2}} \right)}}{4}$$
-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
$$- \frac{x}{2 x^{2} + 4} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4}$$
-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
$$\frac{\sqrt{2} x^{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} - 2 x + 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4 x^{2} + 8}$$
(-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
$$- \frac{x}{2 x^{2} + 4} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4}$$
-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 /
$$\frac{\sqrt{2} x^{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} - 2 x + 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4 \left(x^{2} + 2\right)}$$
(-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 /
$$\frac{- 2 x + \sqrt{2} \left(x^{2} + 2\right) \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}}{4 \left(x^{2} + 2\right)}$$
(-2*x + sqrt(2)*(2 + x^2)*atan(x*sqrt(2)/2))/(4*(2 + x^2))