Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
asin(2*x)/(2*sqrt(x))+2*(sqrt(x)+1/2)/sqrt(1-4*x^2)
¿Cómo vas a descomponer esta asin(2*x)/(2*sqrt(x))+2*(sqrt(x)+1/2)/sqrt(1-4*x^2) expresión en fracciones?
Solución
Ha introducido
[src]
/ ___ 1\
2*|\/ x + -|
asin(2*x) \ 2/
--------- + -------------
___ __________
2*\/ x / 2
\/ 1 - 4*x
$$\frac{2 \left(\sqrt{x} + \frac{1}{2}\right)}{\sqrt{1 - 4 x^{2}}} + \frac{\operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x}}$$
asin(2*x)/((2*sqrt(x))) + (2*(sqrt(x) + 1/2))/sqrt(1 - 4*x^2)
Simplificación general
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__________
/ 2
___ \/ 1 - 4*x *asin(2*x)
\/ x + 2*x + -----------------------
2
-------------------------------------
__________
___ / 2
\/ x *\/ 1 - 4*x
$$\frac{\sqrt{x} + 2 x + \frac{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}{2}}{\sqrt{x} \sqrt{1 - 4 x^{2}}}$$
(sqrt(x) + 2*x + sqrt(1 - 4*x^2)*asin(2*x)/2)/(sqrt(x)*sqrt(1 - 4*x^2))
Respuesta numérica
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0.5*x^(-0.5)*asin(2*x) + 0.5*(0.25 - x^2)^(-0.5)*(1.0 + 2.0*x^0.5)
0.5*x^(-0.5)*asin(2*x) + 0.5*(0.25 - x^2)^(-0.5)*(1.0 + 2.0*x^0.5)
Combinatoria
[src]
__________
___ / 2
2*\/ x + 4*x + \/ 1 - 4*x *asin(2*x)
---------------------------------------
___ _______________________
2*\/ x *\/ -(1 + 2*x)*(-1 + 2*x)
$$\frac{2 \sqrt{x} + 4 x + \sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x} \sqrt{- \left(2 x - 1\right) \left(2 x + 1\right)}}$$
(2*sqrt(x) + 4*x + sqrt(1 - 4*x^2)*asin(2*x))/(2*sqrt(x)*sqrt(-(1 + 2*x)*(-1 + 2*x)))
Parte trigonométrica
[src]
___ 1 + 2*\/ x asin(2*x) ------------- + --------- __________ ___ / 2 2*\/ x \/ 1 - 4*x
$$\frac{2 \sqrt{x} + 1}{\sqrt{1 - 4 x^{2}}} + \frac{\operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x}}$$
(1 + 2*sqrt(x))/sqrt(1 - 4*x^2) + asin(2*x)/(2*sqrt(x))
Potencias
[src]
___ 1 + 2*\/ x asin(2*x) ------------- + --------- __________ ___ / 2 2*\/ x \/ 1 - 4*x
$$\frac{2 \sqrt{x} + 1}{\sqrt{1 - 4 x^{2}}} + \frac{\operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x}}$$
(1 + 2*sqrt(x))/sqrt(1 - 4*x^2) + asin(2*x)/(2*sqrt(x))
Denominador común
[src]
__________
___ / 2
2*\/ x + 4*x + \/ 1 - 4*x *asin(2*x)
---------------------------------------
__________
___ / 2
2*\/ x *\/ 1 - 4*x
$$\frac{2 \sqrt{x} + 4 x + \sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x} \sqrt{1 - 4 x^{2}}}$$
(2*sqrt(x) + 4*x + sqrt(1 - 4*x^2)*asin(2*x))/(2*sqrt(x)*sqrt(1 - 4*x^2))
Denominador racional
[src]
__________ __________
/ 2 ___ / 2 2
-2*asin(2*x) - 8*x*\/ 1 - 4*x - 4*\/ x *\/ 1 - 4*x + 8*x *asin(2*x)
-------------------------------------------------------------------------
___ / 2\
4*\/ x *\-1 + 4*x /
$$\frac{- 4 \sqrt{x} \sqrt{1 - 4 x^{2}} + 8 x^{2} \operatorname{asin}{\left(2 x \right)} - 8 x \sqrt{1 - 4 x^{2}} - 2 \operatorname{asin}{\left(2 x \right)}}{4 \sqrt{x} \left(4 x^{2} - 1\right)}$$
(-2*asin(2*x) - 8*x*sqrt(1 - 4*x^2) - 4*sqrt(x)*sqrt(1 - 4*x^2) + 8*x^2*asin(2*x))/(4*sqrt(x)*(-1 + 4*x^2))
Compilar la expresión
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___ 1 + 2*\/ x asin(2*x) ------------- + --------- __________ ___ / 2 2*\/ x \/ 1 - 4*x
$$\frac{2 \sqrt{x} + 1}{\sqrt{1 - 4 x^{2}}} + \frac{\operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x}}$$
(1 + 2*sqrt(x))/sqrt(1 - 4*x^2) + asin(2*x)/(2*sqrt(x))
Unión de expresiones racionales
[src]
__________
/ 2 ___ / ___\
\/ 1 - 4*x *asin(2*x) + 2*\/ x *\1 + 2*\/ x /
-----------------------------------------------
__________
___ / 2
2*\/ x *\/ 1 - 4*x
$$\frac{2 \sqrt{x} \left(2 \sqrt{x} + 1\right) + \sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}{2 \sqrt{x} \sqrt{1 - 4 x^{2}}}$$
(sqrt(1 - 4*x^2)*asin(2*x) + 2*sqrt(x)*(1 + 2*sqrt(x)))/(2*sqrt(x)*sqrt(1 - 4*x^2))