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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
acot(x)   log(2*x)
------- - --------
   x            2 
           1 + x
−log⁡(2x)x2+1+acot⁡(x)x- \frac{\log{\left(2 x \right)}}{x^{2} + 1} + \frac{\operatorname{acot}{\left(x \right)}}{x} 
acot(x)/x - log(2*x)/(1 + x^2)
Simplificación general [src] 
/     2\                     
\1 + x /*acot(x) - x*log(2*x)
-----------------------------
            /     2\         
          x*\1 + x /
−xlog⁡(2x)+(x2+1)acot⁡(x)x(x2+1)\frac{- x \log{\left(2 x \right)} + \left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}{x \left(x^{2} + 1\right)} 
((1 + x^2)*acot(x) - x*log(2*x))/(x*(1 + x^2))
Respuesta numérica [src] 
acot(x)/x - log(2*x)/(1.0 + x^2)
acot(x)/x - log(2*x)/(1.0 + x^2)
Combinatoria [src] 
 2                                        
x *acot(x) - x*log(2) - x*log(x) + acot(x)
------------------------------------------
                  /     2\                
                x*\1 + x /
x2acot⁡(x)−xlog⁡(x)−xlog⁡(2)+acot⁡(x)x(x2+1)\frac{x^{2} \operatorname{acot}{\left(x \right)} - x \log{\left(x \right)} - x \log{\left(2 \right)} + \operatorname{acot}{\left(x \right)}}{x \left(x^{2} + 1\right)} 
(x^2*acot(x) - x*log(2) - x*log(x) + acot(x))/(x*(1 + x^2))
Denominador común [src] 
 2                                        
x *acot(x) - x*log(2) - x*log(x) + acot(x)
------------------------------------------
                       3                  
                  x + x
x2acot⁡(x)−xlog⁡(x)−xlog⁡(2)+acot⁡(x)x3+x\frac{x^{2} \operatorname{acot}{\left(x \right)} - x \log{\left(x \right)} - x \log{\left(2 \right)} + \operatorname{acot}{\left(x \right)}}{x^{3} + x} 
(x^2*acot(x) - x*log(2) - x*log(x) + acot(x))/(x + x^3)
Denominador racional [src] 
/     2\                     
\1 + x /*acot(x) - x*log(2*x)
-----------------------------
            /     2\         
          x*\1 + x /
−xlog⁡(2x)+(x2+1)acot⁡(x)x(x2+1)\frac{- x \log{\left(2 x \right)} + \left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}{x \left(x^{2} + 1\right)} 
((1 + x^2)*acot(x) - x*log(2*x))/(x*(1 + x^2))
Unión de expresiones racionales [src] 
/     2\                     
\1 + x /*acot(x) - x*log(2*x)
-----------------------------
            /     2\         
          x*\1 + x /
−xlog⁡(2x)+(x2+1)acot⁡(x)x(x2+1)\frac{- x \log{\left(2 x \right)} + \left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}{x \left(x^{2} + 1\right)} 
((1 + x^2)*acot(x) - x*log(2*x))/(x*(1 + x^2))
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