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