Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
asin(x)^2*(10-2*x)/(5-x)^4+2*asin(x)/(sqrt(1-x^2)*(5-x)^2)
¿Cómo vas a descomponer esta asin(x)^2*(10-2*x)/(5-x)^4+2*asin(x)/(sqrt(1-x^2)*(5-x)^2) expresión en fracciones?
Solución
Ha introducido
[src]
2
asin (x)*(10 - 2*x) 2*asin(x)
------------------- + --------------------
4 ________
(5 - x) / 2 2
\/ 1 - x *(5 - x)
$$\frac{\left(10 - 2 x\right) \operatorname{asin}^{2}{\left(x \right)}}{\left(5 - x\right)^{4}} + \frac{2 \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(5 - x\right)^{2}}$$
(asin(x)^2*(10 - 2*x))/(5 - x)^4 + (2*asin(x))/((sqrt(1 - x^2)*(5 - x)^2))
Simplificación general
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/ ________ \
| 2 / 2 |
2*\(-5 + x) + \/ 1 - x *(5 - x)*asin(x)/*asin(x)
---------------------------------------------------
________
/ 2 4
\/ 1 - x *(-5 + x)
$$\frac{2 \left(\sqrt{1 - x^{2}} \left(5 - x\right) \operatorname{asin}{\left(x \right)} + \left(x - 5\right)^{2}\right) \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x - 5\right)^{4}}$$
2*((-5 + x)^2 + sqrt(1 - x^2)*(5 - x)*asin(x))*asin(x)/(sqrt(1 - x^2)*(-5 + x)^4)
Respuesta numérica
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0.08*(1.0 - x^2)^(-0.5)*asin(x)/(1 - 0.2*x)^2 + 0.0016*asin(x)^2*(10.0 - 2.0*x)/(1 - 0.2*x)^4
0.08*(1.0 - x^2)^(-0.5)*asin(x)/(1 - 0.2*x)^2 + 0.0016*asin(x)^2*(10.0 - 2.0*x)/(1 - 0.2*x)^4
Denominador común
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________
/ 2 2
-10*asin(x) - 2*\/ 1 - x *asin (x) + 2*x*asin(x)
-------------------------------------------------------------------------
________ ________ ________ ________
/ 2 3 / 2 2 / 2 / 2
- 125*\/ 1 - x + x *\/ 1 - x - 15*x *\/ 1 - x + 75*x*\/ 1 - x
$$\frac{2 x \operatorname{asin}{\left(x \right)} - 2 \sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)} - 10 \operatorname{asin}{\left(x \right)}}{x^{3} \sqrt{1 - x^{2}} - 15 x^{2} \sqrt{1 - x^{2}} + 75 x \sqrt{1 - x^{2}} - 125 \sqrt{1 - x^{2}}}$$
(-10*asin(x) - 2*sqrt(1 - x^2)*asin(x)^2 + 2*x*asin(x))/(-125*sqrt(1 - x^2) + x^3*sqrt(1 - x^2) - 15*x^2*sqrt(1 - x^2) + 75*x*sqrt(1 - x^2))
Denominador racional
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________
2 2 3 2 2 / 2 4 2 2 2 2 2
- 10*(-5 + x) *asin (x) - 2*x *(-5 + x) *asin (x) - 2*\/ 1 - x *(-5 + x) *asin(x) + 2*x*(-5 + x) *asin (x) + 10*x *(-5 + x) *asin (x)
---------------------------------------------------------------------------------------------------------------------------------------
/ 2\ 6
\-1 + x /*(-5 + x)
$$\frac{- 2 x^{3} \left(x - 5\right)^{2} \operatorname{asin}^{2}{\left(x \right)} + 10 x^{2} \left(x - 5\right)^{2} \operatorname{asin}^{2}{\left(x \right)} + 2 x \left(x - 5\right)^{2} \operatorname{asin}^{2}{\left(x \right)} - 2 \sqrt{1 - x^{2}} \left(x - 5\right)^{4} \operatorname{asin}{\left(x \right)} - 10 \left(x - 5\right)^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(x - 5\right)^{6} \left(x^{2} - 1\right)}$$
(-10*(-5 + x)^2*asin(x)^2 - 2*x^3*(-5 + x)^2*asin(x)^2 - 2*sqrt(1 - x^2)*(-5 + x)^4*asin(x) + 2*x*(-5 + x)^2*asin(x)^2 + 10*x^2*(-5 + x)^2*asin(x)^2)/((-1 + x^2)*(-5 + x)^6)
Unión de expresiones racionales
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/ ________ \
| / 2 |
2*\5 - x + \/ 1 - x *asin(x)/*asin(x)
---------------------------------------
________
/ 2 3
\/ 1 - x *(5 - x)
$$\frac{2 \left(- x + \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} + 5\right) \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(5 - x\right)^{3}}$$
2*(5 - x + sqrt(1 - x^2)*asin(x))*asin(x)/(sqrt(1 - x^2)*(5 - x)^3)
Combinatoria
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/ ________ \
| / 2 |
2*\-5 + x - \/ 1 - x *asin(x)/*asin(x)
----------------------------------------
___________________ 3
\/ -(1 + x)*(-1 + x) *(-5 + x)
$$\frac{2 \left(x - \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} - 5\right) \operatorname{asin}{\left(x \right)}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(x - 5\right)^{3}}$$
2*(-5 + x - sqrt(1 - x^2)*asin(x))*asin(x)/(sqrt(-(1 + x)*(-1 + x))*(-5 + x)^3)