Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
asin(5*x)^4/(3*(x-4)^(2/3))+20*(x-4)^(1/3)*asin(5*x)^3/sqrt(1-25*x^2)
¿Cómo vas a descomponer esta asin(5*x)^4/(3*(x-4)^(2/3))+20*(x-4)^(1/3)*asin(5*x)^3/sqrt(1-25*x^2) expresión en fracciones?
Solución
Ha introducido
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4 3 _______ 3
asin (5*x) 20*\/ x - 4 *asin (5*x)
------------ + -----------------------
2/3 ___________
3*(x - 4) / 2
\/ 1 - 25*x
$$\frac{20 \sqrt[3]{x - 4} \operatorname{asin}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}} + \frac{\operatorname{asin}^{4}{\left(5 x \right)}}{3 \left(x - 4\right)^{\frac{2}{3}}}$$
asin(5*x)^4/((3*(x - 4)^(2/3))) + ((20*(x - 4)^(1/3))*asin(5*x)^3)/sqrt(1 - 25*x^2)
Simplificación general
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/ ___________ \
3 | / 2 |
asin (5*x)*\-240 + 60*x + \/ 1 - 25*x *asin(5*x)/
---------------------------------------------------
___________
/ 2 2/3
3*\/ 1 - 25*x *(-4 + x)
$$\frac{\left(60 x + \sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)} - 240\right) \operatorname{asin}^{3}{\left(5 x \right)}}{3 \sqrt{1 - 25 x^{2}} \left(x - 4\right)^{\frac{2}{3}}}$$
asin(5*x)^3*(-240 + 60*x + sqrt(1 - 25*x^2)*asin(5*x))/(3*sqrt(1 - 25*x^2)*(-4 + x)^(2/3))
Respuesta numérica
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0.13228342099735*(-1 + 0.25*x)^(-0.666666666666667)*asin(5*x)^4 + 6.3496042078728*(-1 + 0.25*x)^0.333333333333333*(0.04 - x^2)^(-0.5)*asin(5*x)^3
0.13228342099735*(-1 + 0.25*x)^(-0.666666666666667)*asin(5*x)^4 + 6.3496042078728*(-1 + 0.25*x)^0.333333333333333*(0.04 - x^2)^(-0.5)*asin(5*x)^3
Denominador racional
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___________ ___________
4 2 4 / 2 3 / 2 3
- asin (5*x) + 25*x *asin (5*x) + 240*\/ 1 - 25*x *asin (5*x) - 60*x*\/ 1 - 25*x *asin (5*x)
------------------------------------------------------------------------------------------------
/ 2\ 2/3
3*\-1 + 25*x /*(-4 + x)
$$\frac{25 x^{2} \operatorname{asin}^{4}{\left(5 x \right)} - 60 x \sqrt{1 - 25 x^{2}} \operatorname{asin}^{3}{\left(5 x \right)} + 240 \sqrt{1 - 25 x^{2}} \operatorname{asin}^{3}{\left(5 x \right)} - \operatorname{asin}^{4}{\left(5 x \right)}}{3 \left(x - 4\right)^{\frac{2}{3}} \left(25 x^{2} - 1\right)}$$
(-asin(5*x)^4 + 25*x^2*asin(5*x)^4 + 240*sqrt(1 - 25*x^2)*asin(5*x)^3 - 60*x*sqrt(1 - 25*x^2)*asin(5*x)^3)/(3*(-1 + 25*x^2)*(-4 + x)^(2/3))
Potencias
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4 3 ________ 3
asin (5*x) 20*\/ -4 + x *asin (5*x)
------------- + ------------------------
2/3 ___________
3*(-4 + x) / 2
\/ 1 - 25*x
$$\frac{\operatorname{asin}^{4}{\left(5 x \right)}}{3 \left(x - 4\right)^{\frac{2}{3}}} + \frac{20 \sqrt[3]{x - 4} \operatorname{asin}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}$$
asin(5*x)^4/(3*(-4 + x)^(2/3)) + 20*(-4 + x)^(1/3)*asin(5*x)^3/sqrt(1 - 25*x^2)
Compilar la expresión
[src]
4 3 ________ 3
asin (5*x) 20*\/ -4 + x *asin (5*x)
------------- + ------------------------
2/3 ___________
3*(-4 + x) / 2
\/ 1 - 25*x
$$\frac{\operatorname{asin}^{4}{\left(5 x \right)}}{3 \left(x - 4\right)^{\frac{2}{3}}} + \frac{20 \sqrt[3]{x - 4} \operatorname{asin}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}$$
asin(5*x)^4/(3*(-4 + x)^(2/3)) + 20*(-4 + x)^(1/3)*asin(5*x)^3/sqrt(1 - 25*x^2)
Denominador común
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___________
3 / 2 4 3
- 240*asin (5*x) + \/ 1 - 25*x *asin (5*x) + 60*x*asin (5*x)
--------------------------------------------------------------
___________
/ 2 2/3
3*\/ 1 - 25*x *(-4 + x)
$$\frac{60 x \operatorname{asin}^{3}{\left(5 x \right)} + \sqrt{1 - 25 x^{2}} \operatorname{asin}^{4}{\left(5 x \right)} - 240 \operatorname{asin}^{3}{\left(5 x \right)}}{3 \sqrt{1 - 25 x^{2}} \left(x - 4\right)^{\frac{2}{3}}}$$
(-240*asin(5*x)^3 + sqrt(1 - 25*x^2)*asin(5*x)^4 + 60*x*asin(5*x)^3)/(3*sqrt(1 - 25*x^2)*(-4 + x)^(2/3))
Unión de expresiones racionales
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/ ___________ \
3 | / 2 |
asin (5*x)*\-240 + 60*x + \/ 1 - 25*x *asin(5*x)/
---------------------------------------------------
___________
/ 2 2/3
3*\/ 1 - 25*x *(-4 + x)
$$\frac{\left(60 x + \sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)} - 240\right) \operatorname{asin}^{3}{\left(5 x \right)}}{3 \sqrt{1 - 25 x^{2}} \left(x - 4\right)^{\frac{2}{3}}}$$
asin(5*x)^3*(-240 + 60*x + sqrt(1 - 25*x^2)*asin(5*x))/(3*sqrt(1 - 25*x^2)*(-4 + x)^(2/3))
Combinatoria
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/ ___________ \
3 | / 2 |
asin (5*x)*\-240 + 60*x + \/ 1 - 25*x *asin(5*x)/
---------------------------------------------------
_______________________ 2/3
3*\/ -(1 + 5*x)*(-1 + 5*x) *(-4 + x)
$$\frac{\left(60 x + \sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)} - 240\right) \operatorname{asin}^{3}{\left(5 x \right)}}{3 \sqrt{- \left(5 x - 1\right) \left(5 x + 1\right)} \left(x - 4\right)^{\frac{2}{3}}}$$
asin(5*x)^3*(-240 + 60*x + sqrt(1 - 25*x^2)*asin(5*x))/(3*sqrt(-(1 + 5*x)*(-1 + 5*x))*(-4 + x)^(2/3))
Parte trigonométrica
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4 3 ________ 3
asin (5*x) 20*\/ -4 + x *asin (5*x)
------------- + ------------------------
2/3 ___________
3*(-4 + x) / 2
\/ 1 - 25*x
$$\frac{\operatorname{asin}^{4}{\left(5 x \right)}}{3 \left(x - 4\right)^{\frac{2}{3}}} + \frac{20 \sqrt[3]{x - 4} \operatorname{asin}^{3}{\left(5 x \right)}}{\sqrt{1 - 25 x^{2}}}$$
asin(5*x)^4/(3*(-4 + x)^(2/3)) + 20*(-4 + x)^(1/3)*asin(5*x)^3/sqrt(1 - 25*x^2)