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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?

Expresión a simplificar:

Solución

Ha introducido [src] 
    log(x)        /log(atan(x + 1))             log(x)          \
atan      (x + 1)*|---------------- + --------------------------|
                  |       x           /           2\            |
                  \                   \1 + (x + 1) /*atan(x + 1)/
(log⁡(x)((x+1)2+1)atan⁡(x+1)+log⁡(atan⁡(x+1))x)atan⁡log⁡(x)(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) /
(xlog⁡(x)+((x+1)2+1)log⁡(atan⁡(x+1))atan⁡(x+1))atan⁡log⁡(x)−1(x+1)x((x+1)2+1)\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))
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                                                                  3                                    2                                                                              
                                                                 x *atan(1 + x) + 2*x*atan(1 + x) + 2*x *atan(1 + x)
x2log⁡(atan⁡(x+1))atan⁡(x+1)atan⁡log⁡(x)(x+1)+xlog⁡(x)atan⁡log⁡(x)(x+1)+2xlog⁡(atan⁡(x+1))atan⁡(x+1)atan⁡log⁡(x)(x+1)+2log⁡(atan⁡(x+1))atan⁡(x+1)atan⁡log⁡(x)(x+1)x3atan⁡(x+1)+2x2atan⁡(x+1)+2xatan⁡(x+1)\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/
xlog⁡(x)atan⁡log⁡(x)−1(x+1)+(x+1)2log⁡(atan⁡(x+1))atan⁡(x+1)atan⁡log⁡(x)−1(x+1)+log⁡(atan⁡(x+1))atan⁡(x+1)atan⁡log⁡(x)−1(x+1)x(x2+2x+2)\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)
(xlog⁡(x)+((x+1)2+1)log⁡(atan⁡(x+1))atan⁡(x+1))atan⁡log⁡(x)(x+1)x((x+1)2+1)atan⁡(x+1)\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)
(x2log⁡(atan⁡(x+1))atan⁡(x+1)+xlog⁡(x)+2xlog⁡(atan⁡(x+1))atan⁡(x+1)+2log⁡(atan⁡(x+1))atan⁡(x+1))atan⁡log⁡(x)(x+1)x(x2+2x+2)atan⁡(x+1)\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))
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