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Simplificación de expresiones/ Descomposición en fracciones simples/ atan(2*x)/x+2*log(x)/(1+4*x^2)

¿Cómo vas a descomponer esta atan(2*x)/x+2*log(x)/(1+4*x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
atan(2*x)   2*log(x)
--------- + --------
    x              2
            1 + 4*x
2log⁡(x)4x2+1+atan⁡(2x)x\frac{2 \log{\left(x \right)}}{4 x^{2} + 1} + \frac{\operatorname{atan}{\left(2 x \right)}}{x} 
atan(2*x)/x + (2*log(x))/(1 + 4*x^2)
Simplificación general [src] 
/       2\                       
\1 + 4*x /*atan(2*x) + 2*x*log(x)
---------------------------------
             /       2\          
           x*\1 + 4*x /
2xlog⁡(x)+(4x2+1)atan⁡(2x)x(4x2+1)\frac{2 x \log{\left(x \right)} + \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}{x \left(4 x^{2} + 1\right)} 
((1 + 4*x^2)*atan(2*x) + 2*x*log(x))/(x*(1 + 4*x^2))
Respuesta numérica [src] 
atan(2*x)/x + 2.0*log(x)/(1.0 + 4.0*x^2)
atan(2*x)/x + 2.0*log(x)/(1.0 + 4.0*x^2)
Denominador racional [src] 
/       2\                       
\1 + 4*x /*atan(2*x) + 2*x*log(x)
---------------------------------
             /       2\          
           x*\1 + 4*x /
2xlog⁡(x)+(4x2+1)atan⁡(2x)x(4x2+1)\frac{2 x \log{\left(x \right)} + \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}{x \left(4 x^{2} + 1\right)} 
((1 + 4*x^2)*atan(2*x) + 2*x*log(x))/(x*(1 + 4*x^2))
Unión de expresiones racionales [src] 
/       2\                       
\1 + 4*x /*atan(2*x) + 2*x*log(x)
---------------------------------
             /       2\          
           x*\1 + 4*x /
2xlog⁡(x)+(4x2+1)atan⁡(2x)x(4x2+1)\frac{2 x \log{\left(x \right)} + \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}{x \left(4 x^{2} + 1\right)} 
((1 + 4*x^2)*atan(2*x) + 2*x*log(x))/(x*(1 + 4*x^2))
Denominador común [src] 
                2                      
2*x*log(x) + 4*x *atan(2*x) + atan(2*x)
---------------------------------------
                       3               
                x + 4*x
4x2atan⁡(2x)+2xlog⁡(x)+atan⁡(2x)4x3+x\frac{4 x^{2} \operatorname{atan}{\left(2 x \right)} + 2 x \log{\left(x \right)} + \operatorname{atan}{\left(2 x \right)}}{4 x^{3} + x} 
(2*x*log(x) + 4*x^2*atan(2*x) + atan(2*x))/(x + 4*x^3)
Combinatoria [src] 
                2                      
2*x*log(x) + 4*x *atan(2*x) + atan(2*x)
---------------------------------------
                /       2\             
              x*\1 + 4*x /
4x2atan⁡(2x)+2xlog⁡(x)+atan⁡(2x)x(4x2+1)\frac{4 x^{2} \operatorname{atan}{\left(2 x \right)} + 2 x \log{\left(x \right)} + \operatorname{atan}{\left(2 x \right)}}{x \left(4 x^{2} + 1\right)} 
(2*x*log(x) + 4*x^2*atan(2*x) + atan(2*x))/(x*(1 + 4*x^2))
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