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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x)+(4*x^3)/3-(5*x^2)/2+x-1/(2*x^2)

¿Cómo vas a descomponer esta log(x)+(4*x^3)/3-(5*x^2)/2+x-1/(2*x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
            3      2           
         4*x    5*x         1  
log(x) + ---- - ---- + x - ----
          3      2            2
                           2*x
$$\left(x + \left(- \frac{5 x^{2}}{2} + \left(\frac{4 x^{3}}{3} + \log{\left(x \right)}\right)\right)\right) - \frac{1}{2 x^{2}}$$ 
log(x) + (4*x^3)/3 - 5*x^2/2 + x - 1/(2*x^2)
Simplificación general [src] 
       2             3         
    5*x     1     4*x          
x - ---- - ---- + ---- + log(x)
     2        2    3           
           2*x
$$\frac{4 x^{3}}{3} - \frac{5 x^{2}}{2} + x + \log{\left(x \right)} - \frac{1}{2 x^{2}}$$ 
x - 5*x^2/2 - 1/(2*x^2) + 4*x^3/3 + log(x)
Respuesta numérica [src] 
x + 1.33333333333333*x^3 - 0.5/x^2 - 2.5*x^2 + log(x)
x + 1.33333333333333*x^3 - 0.5/x^2 - 2.5*x^2 + log(x)
Unión de expresiones racionales [src] 
      2 /      2                       3\
-3 + x *\- 15*x  + 6*x + 6*log(x) + 8*x /
-----------------------------------------
                      2                  
                   6*x
$$\frac{x^{2} \left(8 x^{3} - 15 x^{2} + 6 x + 6 \log{\left(x \right)}\right) - 3}{6 x^{2}}$$ 
(-3 + x^2*(-15*x^2 + 6*x + 6*log(x) + 8*x^3))/(6*x^2)
Combinatoria [src] 
         4      3      5      2       
-3 - 15*x  + 6*x  + 8*x  + 6*x *log(x)
--------------------------------------
                    2                 
                 6*x
$$\frac{8 x^{5} - 15 x^{4} + 6 x^{3} + 6 x^{2} \log{\left(x \right)} - 3}{6 x^{2}}$$ 
(-3 - 15*x^4 + 6*x^3 + 8*x^5 + 6*x^2*log(x))/(6*x^2)
Denominador común [src] 
       2             3         
    5*x     1     4*x          
x - ---- - ---- + ---- + log(x)
     2        2    3           
           2*x
$$\frac{4 x^{3}}{3} - \frac{5 x^{2}}{2} + x + \log{\left(x \right)} - \frac{1}{2 x^{2}}$$ 
x - 5*x^2/2 - 1/(2*x^2) + 4*x^3/3 + log(x)
Parte trigonométrica [src] 
       2             3         
    5*x     1     4*x          
x - ---- - ---- + ---- + log(x)
     2        2    3           
           2*x
$$\frac{4 x^{3}}{3} - \frac{5 x^{2}}{2} + x + \log{\left(x \right)} - \frac{1}{2 x^{2}}$$ 
x - 5*x^2/2 - 1/(2*x^2) + 4*x^3/3 + log(x)
Denominador racional [src] 
        2 /      2                       3\
-6 + 2*x *\- 15*x  + 6*x + 6*log(x) + 8*x /
-------------------------------------------
                       2                   
                   12*x
$$\frac{2 x^{2} \left(8 x^{3} - 15 x^{2} + 6 x + 6 \log{\left(x \right)}\right) - 6}{12 x^{2}}$$ 
(-6 + 2*x^2*(-15*x^2 + 6*x + 6*log(x) + 8*x^3))/(12*x^2)
Potencias [src] 
       2             3         
    5*x     1     4*x          
x - ---- - ---- + ---- + log(x)
     2        2    3           
           2*x
$$\frac{4 x^{3}}{3} - \frac{5 x^{2}}{2} + x + \log{\left(x \right)} - \frac{1}{2 x^{2}}$$ 
x - 5*x^2/2 - 1/(2*x^2) + 4*x^3/3 + log(x)
Abrimos la expresión [src] 
              3      2         
     1     4*x    5*x          
x - ---- + ---- - ---- + log(x)
       2    3      2           
    2*x
$$x - \frac{5 x^{2}}{2} + \frac{4 x^{3}}{3} + \log{\left(x \right)} - \frac{1}{2 x^{2}}$$ 
x - 1/(2*x^2) + (4*x^3)/3 - 5*x^2/2 + log(x)
Compilar la expresión [src] 
       2             3         
    5*x     1     4*x          
x - ---- - ---- + ---- + log(x)
     2        2    3           
           2*x
$$\frac{4 x^{3}}{3} - \frac{5 x^{2}}{2} + x + \log{\left(x \right)} - \frac{1}{2 x^{2}}$$ 
x - 5*x^2/2 - 1/(2*x^2) + 4*x^3/3 + log(x)
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