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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
atan(x)   log(x)
------- + ------
   x           2
          1 + x
log⁡(x)x2+1+atan⁡(x)x\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x} 
atan(x)/x + log(x)/(1 + x^2)
Simplificación general [src] 
           /     2\        
x*log(x) + \1 + x /*atan(x)
---------------------------
           /     2\        
         x*\1 + x /
xlog⁡(x)+(x2+1)atan⁡(x)x(x2+1)\frac{x \log{\left(x \right)} + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} 
(x*log(x) + (1 + x^2)*atan(x))/(x*(1 + x^2))
Respuesta numérica [src] 
atan(x)/x + log(x)/(1.0 + x^2)
atan(x)/x + log(x)/(1.0 + x^2)
Unión de expresiones racionales [src] 
           /     2\        
x*log(x) + \1 + x /*atan(x)
---------------------------
           /     2\        
         x*\1 + x /
xlog⁡(x)+(x2+1)atan⁡(x)x(x2+1)\frac{x \log{\left(x \right)} + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} 
(x*log(x) + (1 + x^2)*atan(x))/(x*(1 + x^2))
Combinatoria [src] 
            2                  
x*log(x) + x *atan(x) + atan(x)
-------------------------------
             /     2\          
           x*\1 + x /
x2atan⁡(x)+xlog⁡(x)+atan⁡(x)x(x2+1)\frac{x^{2} \operatorname{atan}{\left(x \right)} + x \log{\left(x \right)} + \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} 
(x*log(x) + x^2*atan(x) + atan(x))/(x*(1 + x^2))
Denominador común [src] 
            2                  
x*log(x) + x *atan(x) + atan(x)
-------------------------------
                  3            
             x + x
x2atan⁡(x)+xlog⁡(x)+atan⁡(x)x3+x\frac{x^{2} \operatorname{atan}{\left(x \right)} + x \log{\left(x \right)} + \operatorname{atan}{\left(x \right)}}{x^{3} + x} 
(x*log(x) + x^2*atan(x) + atan(x))/(x + x^3)
Denominador racional [src] 
           /     2\        
x*log(x) + \1 + x /*atan(x)
---------------------------
           /     2\        
         x*\1 + x /
xlog⁡(x)+(x2+1)atan⁡(x)x(x2+1)\frac{x \log{\left(x \right)} + \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} 
(x*log(x) + (1 + x^2)*atan(x))/(x*(1 + x^2))
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