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