Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
acos(x)/2+x/sqrt(4-x^2)-x/(2*sqrt(1-x^2))
¿Cómo vas a descomponer esta acos(x)/2+x/sqrt(4-x^2)-x/(2*sqrt(1-x^2)) expresión en fracciones?
Solución
Ha introducido
[src]
acos(x) x x
------- + ----------- - -------------
2 ________ ________
/ 2 / 2
\/ 4 - x 2*\/ 1 - x
$$- \frac{x}{2 \sqrt{1 - x^{2}}} + \left(\frac{x}{\sqrt{4 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{2}\right)$$
acos(x)/2 + x/sqrt(4 - x^2) - x/(2*sqrt(1 - x^2))
Simplificación general
[src]
acos(x) x x
------- + ----------- - -------------
2 ________ ________
/ 2 / 2
\/ 4 - x 2*\/ 1 - x
$$\frac{x}{\sqrt{4 - x^{2}}} - \frac{x}{2 \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{2}$$
acos(x)/2 + x/sqrt(4 - x^2) - x/(2*sqrt(1 - x^2))
Respuesta numérica
[src]
0.5*acos(x) + 0.5*x*(1 - 0.25*x^2)^(-0.5) - 0.5*x*(1.0 - x^2)^(-0.5)
0.5*acos(x) + 0.5*x*(1 - 0.25*x^2)^(-0.5) - 0.5*x*(1.0 - x^2)^(-0.5)
Parte trigonométrica
[src]
acos(x) x x
------- + ----------- - -------------
2 ________ ________
/ 2 / 2
\/ 4 - x 2*\/ 1 - x
$$\frac{x}{\sqrt{4 - x^{2}}} - \frac{x}{2 \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{2}$$
acos(x)/2 + x/sqrt(4 - x^2) - x/(2*sqrt(1 - x^2))
Denominador racional
[src]
________ ________ ________ ________
2 / 2 3 / 2 3 / 2 4 / 2
8*acos(x) - 10*x *acos(x) - 8*x*\/ 1 - x - 4*x *\/ 4 - x + 2*x *\/ 1 - x + 2*x *acos(x) + 4*x*\/ 4 - x
------------------------------------------------------------------------------------------------------------------
/ 2\ / 2\
4*\-1 + x /*\-4 + x /
$$\frac{2 x^{4} \operatorname{acos}{\left(x \right)} + 2 x^{3} \sqrt{1 - x^{2}} - 4 x^{3} \sqrt{4 - x^{2}} - 10 x^{2} \operatorname{acos}{\left(x \right)} - 8 x \sqrt{1 - x^{2}} + 4 x \sqrt{4 - x^{2}} + 8 \operatorname{acos}{\left(x \right)}}{4 \left(x^{2} - 4\right) \left(x^{2} - 1\right)}$$
(8*acos(x) - 10*x^2*acos(x) - 8*x*sqrt(1 - x^2) - 4*x^3*sqrt(4 - x^2) + 2*x^3*sqrt(1 - x^2) + 2*x^4*acos(x) + 4*x*sqrt(4 - x^2))/(4*(-1 + x^2)*(-4 + x^2))
Potencias
[src]
acos(x) x x
------- + ----------- - -------------
2 ________ ________
/ 2 / 2
\/ 4 - x 2*\/ 1 - x
$$\frac{x}{\sqrt{4 - x^{2}}} - \frac{x}{2 \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{2}$$
acos(x)/2 + x/sqrt(4 - x^2) - x/(2*sqrt(1 - x^2))
Compilar la expresión
[src]
acos(x) x x
------- + ----------- - -------------
2 ________ ________
/ 2 / 2
\/ 4 - x 2*\/ 1 - x
$$\frac{x}{\sqrt{4 - x^{2}}} - \frac{x}{2 \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{2}$$
acos(x)/2 + x/sqrt(4 - x^2) - x/(2*sqrt(1 - x^2))
Denominador común
[src]
________ ________
/ 2 / 2
acos(x) - x*\/ 4 - x + 2*x*\/ 1 - x
------- + ---------------------------------
2 ________ ________
/ 2 / 2
2*\/ 1 - x *\/ 4 - x
$$\frac{\operatorname{acos}{\left(x \right)}}{2} + \frac{2 x \sqrt{1 - x^{2}} - x \sqrt{4 - x^{2}}}{2 \sqrt{1 - x^{2}} \sqrt{4 - x^{2}}}$$
acos(x)/2 + (-x*sqrt(4 - x^2) + 2*x*sqrt(1 - x^2))/(2*sqrt(1 - x^2)*sqrt(4 - x^2))
Combinatoria
[src]
________ ________ ________ ________
/ 2 / 2 / 2 / 2
- x*\/ 4 - x + 2*x*\/ 1 - x + \/ 1 - x *\/ 4 - x *acos(x)
-------------------------------------------------------------------
___________________ ___________________
2*\/ -(1 + x)*(-1 + x) *\/ -(-2 + x)*(2 + x)
$$\frac{2 x \sqrt{1 - x^{2}} - x \sqrt{4 - x^{2}} + \sqrt{1 - x^{2}} \sqrt{4 - x^{2}} \operatorname{acos}{\left(x \right)}}{2 \sqrt{- \left(x - 2\right) \left(x + 2\right)} \sqrt{- \left(x - 1\right) \left(x + 1\right)}}$$
(-x*sqrt(4 - x^2) + 2*x*sqrt(1 - x^2) + sqrt(1 - x^2)*sqrt(4 - x^2)*acos(x))/(2*sqrt(-(1 + x)*(-1 + x))*sqrt(-(-2 + x)*(2 + x)))
Unión de expresiones racionales
[src]
________ / ________ \ ________
/ 2 | / 2 | / 2
\/ 1 - x *\2*x + \/ 4 - x *acos(x)/ - x*\/ 4 - x
-------------------------------------------------------
________ ________
/ 2 / 2
2*\/ 1 - x *\/ 4 - x
$$\frac{- x \sqrt{4 - x^{2}} + \sqrt{1 - x^{2}} \left(2 x + \sqrt{4 - x^{2}} \operatorname{acos}{\left(x \right)}\right)}{2 \sqrt{1 - x^{2}} \sqrt{4 - x^{2}}}$$
(sqrt(1 - x^2)*(2*x + sqrt(4 - x^2)*acos(x)) - x*sqrt(4 - x^2))/(2*sqrt(1 - x^2)*sqrt(4 - x^2))