Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
atan(x+1)^log(x)*(log(atan(x+1))/x+log(x)/((1+(x+1)^2)*atan(x+1)))
¿Cómo vas a descomponer esta atan(x+1)^log(x)*(log(atan(x+1))/x+log(x)/((1+(x+1)^2)*atan(x+1))) expresión en fracciones?
Solución
Ha introducido
[src]
log(x) /log(atan(x + 1)) log(x) \
atan (x + 1)*|---------------- + --------------------------|
| x / 2\ |
\ \1 + (x + 1) /*atan(x + 1)/
$$\left(\frac{\log{\left(x \right)}}{\left(\left(x + 1\right)^{2} + 1\right) \operatorname{atan}{\left(x + 1 \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x + 1 \right)} \right)}}{x}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x + 1 \right)}$$
atan(x + 1)^log(x)*(log(atan(x + 1))/x + log(x)/(((1 + (x + 1)^2)*atan(x + 1))))
Simplificación general
[src]
-1 + log(x) / / 2\ \
atan (1 + x)*\x*log(x) + \1 + (1 + x) /*atan(1 + x)*log(atan(1 + x))/
-------------------------------------------------------------------------------
/ 2\
x*\1 + (1 + x) /
$$\frac{\left(x \log{\left(x \right)} + \left(\left(x + 1\right)^{2} + 1\right) \log{\left(\operatorname{atan}{\left(x + 1 \right)} \right)} \operatorname{atan}{\left(x + 1 \right)}\right) \operatorname{atan}^{\log{\left(x \right)} - 1}{\left(x + 1 \right)}}{x \left(\left(x + 1\right)^{2} + 1\right)}$$
atan(1 + x)^(-1 + log(x))*(x*log(x) + (1 + (1 + x)^2)*atan(1 + x)*log(atan(1 + x)))/(x*(1 + (1 + x)^2))
Denominador común
[src]
log(x) log(x) 2 log(x) log(x)
x*atan (1 + x)*log(x) + 2*atan (1 + x)*atan(1 + x)*log(atan(1 + x)) + x *atan (1 + x)*atan(1 + x)*log(atan(1 + x)) + 2*x*atan (1 + x)*atan(1 + x)*log(atan(1 + x))
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 2
x *atan(1 + x) + 2*x*atan(1 + x) + 2*x *atan(1 + x)
$$\frac{x^{2} \log{\left(\operatorname{atan}{\left(x + 1 \right)} \right)} \operatorname{atan}{\left(x + 1 \right)} \operatorname{atan}^{\log{\left(x \right)}}{\left(x + 1 \right)} + x \log{\left(x \right)} \operatorname{atan}^{\log{\left(x \right)}}{\left(x + 1 \right)} + 2 x \log{\left(\operatorname{atan}{\left(x + 1 \right)} \right)} \operatorname{atan}{\left(x + 1 \right)} \operatorname{atan}^{\log{\left(x \right)}}{\left(x + 1 \right)} + 2 \log{\left(\operatorname{atan}{\left(x + 1 \right)} \right)} \operatorname{atan}{\left(x + 1 \right)} \operatorname{atan}^{\log{\left(x \right)}}{\left(x + 1 \right)}}{x^{3} \operatorname{atan}{\left(x + 1 \right)} + 2 x^{2} \operatorname{atan}{\left(x + 1 \right)} + 2 x \operatorname{atan}{\left(x + 1 \right)}}$$
(x*atan(1 + x)^log(x)*log(x) + 2*atan(1 + x)^log(x)*atan(1 + x)*log(atan(1 + x)) + x^2*atan(1 + x)^log(x)*atan(1 + x)*log(atan(1 + x)) + 2*x*atan(1 + x)^log(x)*atan(1 + x)*log(atan(1 + x)))/(x^3*atan(1 + x) + 2*x*atan(1 + x) + 2*x^2*atan(1 + x))
Denominador racional
[src]
-1 + log(x) -1 + log(x) 2 -1 + log(x)
x*atan (1 + x)*log(x) + atan (1 + x)*atan(1 + x)*log(atan(1 + x)) + (1 + x) *atan (1 + x)*atan(1 + x)*log(atan(1 + x))
----------------------------------------------------------------------------------------------------------------------------------------------------
/ 2 \
x*\2 + x + 2*x/
$$\frac{x \log{\left(x \right)} \operatorname{atan}^{\log{\left(x \right)} - 1}{\left(x + 1 \right)} + \left(x + 1\right)^{2} \log{\left(\operatorname{atan}{\left(x + 1 \right)} \right)} \operatorname{atan}{\left(x + 1 \right)} \operatorname{atan}^{\log{\left(x \right)} - 1}{\left(x + 1 \right)} + \log{\left(\operatorname{atan}{\left(x + 1 \right)} \right)} \operatorname{atan}{\left(x + 1 \right)} \operatorname{atan}^{\log{\left(x \right)} - 1}{\left(x + 1 \right)}}{x \left(x^{2} + 2 x + 2\right)}$$
(x*atan(1 + x)^(-1 + log(x))*log(x) + atan(1 + x)^(-1 + log(x))*atan(1 + x)*log(atan(1 + x)) + (1 + x)^2*atan(1 + x)^(-1 + log(x))*atan(1 + x)*log(atan(1 + x)))/(x*(2 + x^2 + 2*x))
Unión de expresiones racionales
[src]
log(x) / / 2\ \
atan (1 + x)*\x*log(x) + \1 + (1 + x) /*atan(1 + x)*log(atan(1 + x))/
--------------------------------------------------------------------------
/ 2\
x*\1 + (1 + x) /*atan(1 + x)
$$\frac{\left(x \log{\left(x \right)} + \left(\left(x + 1\right)^{2} + 1\right) \log{\left(\operatorname{atan}{\left(x + 1 \right)} \right)} \operatorname{atan}{\left(x + 1 \right)}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x + 1 \right)}}{x \left(\left(x + 1\right)^{2} + 1\right) \operatorname{atan}{\left(x + 1 \right)}}$$
atan(1 + x)^log(x)*(x*log(x) + (1 + (1 + x)^2)*atan(1 + x)*log(atan(1 + x)))/(x*(1 + (1 + x)^2)*atan(1 + x))
Respuesta numérica
[src]
atan(x + 1)^log(x)*(log(atan(x + 1))/x + log(x)/((1.0 + (1.0 + x)^2)*atan(x + 1)))
atan(x + 1)^log(x)*(log(atan(x + 1))/x + log(x)/((1.0 + (1.0 + x)^2)*atan(x + 1)))
Combinatoria
[src]
log(x) / 2 \
atan (1 + x)*\x*log(x) + 2*atan(1 + x)*log(atan(1 + x)) + x *atan(1 + x)*log(atan(1 + x)) + 2*x*atan(1 + x)*log(atan(1 + x))/
----------------------------------------------------------------------------------------------------------------------------------
/ 2 \
x*\2 + x + 2*x/*atan(1 + x)
$$\frac{\left(x^{2} \log{\left(\operatorname{atan}{\left(x + 1 \right)} \right)} \operatorname{atan}{\left(x + 1 \right)} + x \log{\left(x \right)} + 2 x \log{\left(\operatorname{atan}{\left(x + 1 \right)} \right)} \operatorname{atan}{\left(x + 1 \right)} + 2 \log{\left(\operatorname{atan}{\left(x + 1 \right)} \right)} \operatorname{atan}{\left(x + 1 \right)}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x + 1 \right)}}{x \left(x^{2} + 2 x + 2\right) \operatorname{atan}{\left(x + 1 \right)}}$$
atan(1 + x)^log(x)*(x*log(x) + 2*atan(1 + x)*log(atan(1 + x)) + x^2*atan(1 + x)*log(atan(1 + x)) + 2*x*atan(1 + x)*log(atan(1 + x)))/(x*(2 + x^2 + 2*x)*atan(1 + x))