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