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Simplificación de expresiones/ Descomposición en fracciones simples/ atan(x)^x*(x/((1+x^2)*atan(x))+log(atan(x)))

¿Cómo vas a descomponer esta atan(x)^x*(x/((1+x^2)*atan(x))+log(atan(x))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    x    /       x                       \
atan (x)*|---------------- + log(atan(x))|
         |/     2\                       |
         \\1 + x /*atan(x)               /
$$\left(\frac{x}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \log{\left(\operatorname{atan}{\left(x \right)} \right)}\right) \operatorname{atan}^{x}{\left(x \right)}$$ 
atan(x)^x*(x/(((1 + x^2)*atan(x))) + log(atan(x)))
Simplificación general [src] 
    -1 + x    /    /     2\                     \
atan      (x)*\x + \1 + x /*atan(x)*log(atan(x))/
-------------------------------------------------
                           2                     
                      1 + x
$$\frac{\left(x + \left(x^{2} + 1\right) \log{\left(\operatorname{atan}{\left(x \right)} \right)} \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}^{x - 1}{\left(x \right)}}{x^{2} + 1}$$ 
atan(x)^(-1 + x)*(x + (1 + x^2)*atan(x)*log(atan(x)))/(1 + x^2)
Respuesta numérica [src] 
atan(x)^x*(x/((1.0 + x^2)*atan(x)) + log(atan(x)))
atan(x)^x*(x/((1.0 + x^2)*atan(x)) + log(atan(x)))
Combinatoria [src] 
    x    /                            2                     \
atan (x)*\x + atan(x)*log(atan(x)) + x *atan(x)*log(atan(x))/
-------------------------------------------------------------
                       /     2\                              
                       \1 + x /*atan(x)
$$\frac{\left(x^{2} \log{\left(\operatorname{atan}{\left(x \right)} \right)} \operatorname{atan}{\left(x \right)} + x + \log{\left(\operatorname{atan}{\left(x \right)} \right)} \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}^{x}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}$$ 
atan(x)^x*(x + atan(x)*log(atan(x)) + x^2*atan(x)*log(atan(x)))/((1 + x^2)*atan(x))
Denominador común [src] 
                                   x        
    x                        x*atan (x)     
atan (x)*log(atan(x)) + --------------------
                         2                  
                        x *atan(x) + atan(x)
$$\frac{x \operatorname{atan}^{x}{\left(x \right)}}{x^{2} \operatorname{atan}{\left(x \right)} + \operatorname{atan}{\left(x \right)}} + \log{\left(\operatorname{atan}{\left(x \right)} \right)} \operatorname{atan}^{x}{\left(x \right)}$$ 
atan(x)^x*log(atan(x)) + x*atan(x)^x/(x^2*atan(x) + atan(x))
Denominador racional [src] 
    x    /    /     2\                     \
atan (x)*\x + \1 + x /*atan(x)*log(atan(x))/
--------------------------------------------
              /     2\                      
              \1 + x /*atan(x)
$$\frac{\left(x + \left(x^{2} + 1\right) \log{\left(\operatorname{atan}{\left(x \right)} \right)} \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}^{x}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}$$ 
atan(x)^x*(x + (1 + x^2)*atan(x)*log(atan(x)))/((1 + x^2)*atan(x))
Unión de expresiones racionales [src] 
    x    /    /     2\                     \
atan (x)*\x + \1 + x /*atan(x)*log(atan(x))/
--------------------------------------------
              /     2\                      
              \1 + x /*atan(x)
$$\frac{\left(x + \left(x^{2} + 1\right) \log{\left(\operatorname{atan}{\left(x \right)} \right)} \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}^{x}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}$$ 
atan(x)^x*(x + (1 + x^2)*atan(x)*log(atan(x)))/((1 + x^2)*atan(x))
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