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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
         log(atan(x))             
         ------------             
              2                   
(atan(x))            *log(atan(x))
----------------------------------
         /     2\                 
         \1 + x /*atan(x)
log⁡(atan⁡(x))atan⁡log⁡(atan⁡(x))2(x)(x2+1)atan⁡(x)\frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)} \operatorname{atan}^{\frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{2}}{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} 
(atan(x)^(log(atan(x))/2)*log(atan(x)))/(((1 + x^2)*atan(x)))
Simplificación general [src] 
              log(atan(x))             
         -1 + ------------             
                   2                   
(atan(x))                 *log(atan(x))
---------------------------------------
                      2                
                 1 + x
log⁡(atan⁡(x))atan⁡log⁡(atan⁡(x))2−1(x)x2+1\frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)} \operatorname{atan}^{\frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{2} - 1}{\left(x \right)}}{x^{2} + 1} 
atan(x)^(-1 + log(atan(x))/2)*log(atan(x))/(1 + x^2)
Respuesta numérica [src] 
atan(x)^(0.5*log(atan(x)))*log(atan(x))/((1.0 + x^2)*atan(x))
atan(x)^(0.5*log(atan(x)))*log(atan(x))/((1.0 + x^2)*atan(x))
Potencias [src] 
              log(atan(x))             
         -1 + ------------             
                   2                   
(atan(x))                 *log(atan(x))
---------------------------------------
                      2                
                 1 + x
log⁡(atan⁡(x))atan⁡log⁡(atan⁡(x))2−1(x)x2+1\frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)} \operatorname{atan}^{\frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{2} - 1}{\left(x \right)}}{x^{2} + 1} 
atan(x)^(-1 + log(atan(x))/2)*log(atan(x))/(1 + x^2)
Denominador racional [src] 
              log(atan(x))             
         -1 + ------------             
                   2                   
(atan(x))                 *log(atan(x))
---------------------------------------
                      2                
                 1 + x
log⁡(atan⁡(x))atan⁡log⁡(atan⁡(x))2−1(x)x2+1\frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)} \operatorname{atan}^{\frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{2} - 1}{\left(x \right)}}{x^{2} + 1} 
atan(x)^(-1 + log(atan(x))/2)*log(atan(x))/(1 + x^2)
Denominador común [src] 
         log(atan(x))             
         ------------             
              2                   
(atan(x))            *log(atan(x))
----------------------------------
        2                         
       x *atan(x) + atan(x)
log⁡(atan⁡(x))atan⁡log⁡(atan⁡(x))2(x)x2atan⁡(x)+atan⁡(x)\frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)} \operatorname{atan}^{\frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{2}}{\left(x \right)}}{x^{2} \operatorname{atan}{\left(x \right)} + \operatorname{atan}{\left(x \right)}} 
atan(x)^(log(atan(x))/2)*log(atan(x))/(x^2*atan(x) + atan(x))
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