Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
asin(x)^(1/(5*x^3-4))*(1/(sqrt(1-x^2)*(5*x^3-4)*asin(x))-15*x^2*log(asin(x))/(5*x^3-4)^2)
¿Cómo vas a descomponer esta asin(x)^(1/(5*x^3-4))*(1/(sqrt(1-x^2)*(5*x^3-4)*asin(x))-15*x^2*log(asin(x))/(5*x^3-4)^2) expresión en fracciones?
Solución
Ha introducido
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1
--------
3 / 2 \
5*x - 4 | 1 15*x *log(asin(x))|
(asin(x)) *|------------------------------ - ------------------|
| ________ 2 |
| / 2 / 3 \ / 3 \ |
\\/ 1 - x *\5*x - 4/*asin(x) \5*x - 4/ /
$$\left(- \frac{15 x^{2} \log{\left(\operatorname{asin}{\left(x \right)} \right)}}{\left(5 x^{3} - 4\right)^{2}} + \frac{1}{\sqrt{1 - x^{2}} \left(5 x^{3} - 4\right) \operatorname{asin}{\left(x \right)}}\right) \operatorname{asin}^{\frac{1}{5 x^{3} - 4}}{\left(x \right)}$$
asin(x)^(1/(5*x^3 - 4))*(1/((sqrt(1 - x^2)*(5*x^3 - 4))*asin(x)) - (15*x^2)*log(asin(x))/(5*x^3 - 4)^2)
Simplificación general
[src]
/ 3\
5*\1 - x /
----------
3 / ________ \
-4 + 5*x | 3 2 / 2 |
(asin(x)) *\-4 + 5*x - 15*x *\/ 1 - x *asin(x)*log(asin(x))/
------------------------------------------------------------------------
________ 2
/ 2 / 3\
\/ 1 - x *\-4 + 5*x /
$$\frac{\left(5 x^{3} - 15 x^{2} \sqrt{1 - x^{2}} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \operatorname{asin}{\left(x \right)} - 4\right) \operatorname{asin}^{\frac{5 \left(1 - x^{3}\right)}{5 x^{3} - 4}}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(5 x^{3} - 4\right)^{2}}$$
asin(x)^(5*(1 - x^3)/(-4 + 5*x^3))*(-4 + 5*x^3 - 15*x^2*sqrt(1 - x^2)*asin(x)*log(asin(x)))/(sqrt(1 - x^2)*(-4 + 5*x^3)^2)
Respuesta numérica
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asin(x)^(1/(-4.0 + 5.0*x^3))*((1.0 - x^2)^(-0.5)/((-4.0 + 5.0*x^3)*asin(x)) - 0.6*x^2*log(asin(x))/(-0.8 + x^3)^2)
asin(x)^(1/(-4.0 + 5.0*x^3))*((1.0 - x^2)^(-0.5)/((-4.0 + 5.0*x^3)*asin(x)) - 0.6*x^2*log(asin(x))/(-0.8 + x^3)^2)
Denominador común
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1 1 1
--------- --------- ---------
3 3 ________ 3
-4 + 5*x 3 -4 + 5*x 2 / 2 -4 + 5*x
- 4*(asin(x)) + 5*x *(asin(x)) - 15*x *\/ 1 - x *(asin(x)) *asin(x)*log(asin(x))
------------------------------------------------------------------------------------------------------------
________ ________ ________
/ 2 3 / 2 6 / 2
16*\/ 1 - x *asin(x) - 40*x *\/ 1 - x *asin(x) + 25*x *\/ 1 - x *asin(x)
$$\frac{5 x^{3} \operatorname{asin}^{\frac{1}{5 x^{3} - 4}}{\left(x \right)} - 15 x^{2} \sqrt{1 - x^{2}} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \operatorname{asin}{\left(x \right)} \operatorname{asin}^{\frac{1}{5 x^{3} - 4}}{\left(x \right)} - 4 \operatorname{asin}^{\frac{1}{5 x^{3} - 4}}{\left(x \right)}}{25 x^{6} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} - 40 x^{3} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} + 16 \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}$$
(-4*asin(x)^(1/(-4 + 5*x^3)) + 5*x^3*asin(x)^(1/(-4 + 5*x^3)) - 15*x^2*sqrt(1 - x^2)*asin(x)^(1/(-4 + 5*x^3))*asin(x)*log(asin(x)))/(16*sqrt(1 - x^2)*asin(x) - 40*x^3*sqrt(1 - x^2)*asin(x) + 25*x^6*sqrt(1 - x^2)*asin(x))
Unión de expresiones racionales
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1
---------
3 / ________ \
-4 + 5*x | 3 2 / 2 |
(asin(x)) *\-4 + 5*x - 15*x *\/ 1 - x *asin(x)*log(asin(x))/
-----------------------------------------------------------------------
________ 2
/ 2 / 3\
\/ 1 - x *\-4 + 5*x / *asin(x)
$$\frac{\left(5 x^{3} - 15 x^{2} \sqrt{1 - x^{2}} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \operatorname{asin}{\left(x \right)} - 4\right) \operatorname{asin}^{\frac{1}{5 x^{3} - 4}}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(5 x^{3} - 4\right)^{2} \operatorname{asin}{\left(x \right)}}$$
asin(x)^(1/(-4 + 5*x^3))*(-4 + 5*x^3 - 15*x^2*sqrt(1 - x^2)*asin(x)*log(asin(x)))/(sqrt(1 - x^2)*(-4 + 5*x^3)^2*asin(x))
Combinatoria
[src]
1
---------
3 / ________ \
-4 + 5*x | 3 2 / 2 |
(asin(x)) *\-4 + 5*x - 15*x *\/ 1 - x *asin(x)*log(asin(x))/
-----------------------------------------------------------------------
2
___________________ / 3\
\/ -(1 + x)*(-1 + x) *\-4 + 5*x / *asin(x)
$$\frac{\left(5 x^{3} - 15 x^{2} \sqrt{1 - x^{2}} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \operatorname{asin}{\left(x \right)} - 4\right) \operatorname{asin}^{\frac{1}{5 x^{3} - 4}}{\left(x \right)}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(5 x^{3} - 4\right)^{2} \operatorname{asin}{\left(x \right)}}$$
asin(x)^(1/(-4 + 5*x^3))*(-4 + 5*x^3 - 15*x^2*sqrt(1 - x^2)*asin(x)*log(asin(x)))/(sqrt(-(1 + x)*(-1 + x))*(-4 + 5*x^3)^2*asin(x))
Denominador racional
[src]
1 1 1 1 1
-1 + -------- -1 + -------- -1 + -------- -1 + -------- -1 + --------
________ 2 3 3 3 3 3
/ 2 / 3\ 5*x - 4 7 5*x - 4 2 5*x - 4 4 5*x - 4 5 5*x - 4
- \/ 1 - x *\-4 + 5*x / *(asin(x)) - 75*x *(asin(x)) *asin(x)*log(asin(x)) - 60*x *(asin(x)) *asin(x)*log(asin(x)) + 60*x *(asin(x)) *asin(x)*log(asin(x)) + 75*x *(asin(x)) *asin(x)*log(asin(x))
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
/ 2\ / 3\
\-1 + x /*\-4 + 5*x /
$$\frac{- 75 x^{7} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \operatorname{asin}{\left(x \right)} \operatorname{asin}^{-1 + \frac{1}{5 x^{3} - 4}}{\left(x \right)} + 75 x^{5} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \operatorname{asin}{\left(x \right)} \operatorname{asin}^{-1 + \frac{1}{5 x^{3} - 4}}{\left(x \right)} + 60 x^{4} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \operatorname{asin}{\left(x \right)} \operatorname{asin}^{-1 + \frac{1}{5 x^{3} - 4}}{\left(x \right)} - 60 x^{2} \log{\left(\operatorname{asin}{\left(x \right)} \right)} \operatorname{asin}{\left(x \right)} \operatorname{asin}^{-1 + \frac{1}{5 x^{3} - 4}}{\left(x \right)} - \sqrt{1 - x^{2}} \left(5 x^{3} - 4\right)^{2} \operatorname{asin}^{-1 + \frac{1}{5 x^{3} - 4}}{\left(x \right)}}{\left(x^{2} - 1\right) \left(5 x^{3} - 4\right)^{3}}$$
(-sqrt(1 - x^2)*(-4 + 5*x^3)^2*asin(x)^(-1 + 1/(5*x^3 - 4)) - 75*x^7*asin(x)^(-1 + 1/(5*x^3 - 4))*asin(x)*log(asin(x)) - 60*x^2*asin(x)^(-1 + 1/(5*x^3 - 4))*asin(x)*log(asin(x)) + 60*x^4*asin(x)^(-1 + 1/(5*x^3 - 4))*asin(x)*log(asin(x)) + 75*x^5*asin(x)^(-1 + 1/(5*x^3 - 4))*asin(x)*log(asin(x)))/((-1 + x^2)*(-4 + 5*x^3)^3)