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Simplificación de expresiones/ Descomposición en fracciones simples/ log((2*x^3-2*sqrt(5))/(2*x^3+2*sqrt(5)))/(6*sqrt(5))

¿Cómo vas a descomponer esta log((2*x^3-2*sqrt(5))/(2*x^3+2*sqrt(5)))/(6*sqrt(5)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /   3       ___\
   |2*x  - 2*\/ 5 |
log|--------------|
   |   3       ___|
   \2*x  + 2*\/ 5 /
-------------------
          ___      
      6*\/ 5
log⁡(2x3−252x3+25)65\frac{\log{\left(\frac{2 x^{3} - 2 \sqrt{5}}{2 x^{3} + 2 \sqrt{5}} \right)}}{6 \sqrt{5}} 
log((2*x^3 - 2*sqrt(5))/(2*x^3 + 2*sqrt(5)))/((6*sqrt(5)))
Descomposición de una fracción [src] 
sqrt(5)*log(-2*sqrt(5)/(2*x^3 + 2*sqrt(5)) + 2*x^3/(2*x^3 + 2*sqrt(5)))/30
5log⁡(2x32x3+25−252x3+25)30\frac{\sqrt{5} \log{\left(\frac{2 x^{3}}{2 x^{3} + 2 \sqrt{5}} - \frac{2 \sqrt{5}}{2 x^{3} + 2 \sqrt{5}} \right)}}{30} 
         /         ___               3     \
  ___    |     2*\/ 5             2*x      |
\/ 5 *log|- -------------- + --------------|
         |     3       ___      3       ___|
         \  2*x  + 2*\/ 5    2*x  + 2*\/ 5 /
--------------------------------------------
                     30
Simplificación general [src] 
         / 3     ___\
  ___    |x  - \/ 5 |
\/ 5 *log|----------|
         |  ___    3|
         \\/ 5  + x /
---------------------
          30
5log⁡(x3−5x3+5)30\frac{\sqrt{5} \log{\left(\frac{x^{3} - \sqrt{5}}{x^{3} + \sqrt{5}} \right)}}{30} 
sqrt(5)*log((x^3 - sqrt(5))/(sqrt(5) + x^3))/30
Denominador racional [src] 
         /     6       ___  3\
  ___    |5 + x  - 2*\/ 5 *x |
\/ 5 *log|-------------------|
         |            6      |
         \      -5 + x       /
------------------------------
              30
5log⁡(x6−25x3+5x6−5)30\frac{\sqrt{5} \log{\left(\frac{x^{6} - 2 \sqrt{5} x^{3} + 5}{x^{6} - 5} \right)}}{30} 
sqrt(5)*log((5 + x^6 - 2*sqrt(5)*x^3)/(-5 + x^6))/30
Unión de expresiones racionales [src] 
         / 3     ___\
  ___    |x  - \/ 5 |
\/ 5 *log|----------|
         |  ___    3|
         \\/ 5  + x /
---------------------
          30
5log⁡(x3−5x3+5)30\frac{\sqrt{5} \log{\left(\frac{x^{3} - \sqrt{5}}{x^{3} + \sqrt{5}} \right)}}{30} 
sqrt(5)*log((x^3 - sqrt(5))/(sqrt(5) + x^3))/30
Combinatoria [src] 
         /         ___               3     \
  ___    |     2*\/ 5             2*x      |
\/ 5 *log|- -------------- + --------------|
         |      ___      3       ___      3|
         \  2*\/ 5  + 2*x    2*\/ 5  + 2*x /
--------------------------------------------
                     30
5log⁡(2x32x3+25−252x3+25)30\frac{\sqrt{5} \log{\left(\frac{2 x^{3}}{2 x^{3} + 2 \sqrt{5}} - \frac{2 \sqrt{5}}{2 x^{3} + 2 \sqrt{5}} \right)}}{30} 
sqrt(5)*log(-2*sqrt(5)/(2*sqrt(5) + 2*x^3) + 2*x^3/(2*sqrt(5) + 2*x^3))/30
Denominador común [src] 
         /     3           ___   \
  ___    |    x          \/ 5    |
\/ 5 *log|---------- - ----------|
         |  ___    3     ___    3|
         \\/ 5  + x    \/ 5  + x /
----------------------------------
                30
5log⁡(x3x3+5−5x3+5)30\frac{\sqrt{5} \log{\left(\frac{x^{3}}{x^{3} + \sqrt{5}} - \frac{\sqrt{5}}{x^{3} + \sqrt{5}} \right)}}{30} 
sqrt(5)*log(x^3/(sqrt(5) + x^3) - sqrt(5)/(sqrt(5) + x^3))/30
Parte trigonométrica [src] 
         /      ___      3\
  ___    |- 2*\/ 5  + 2*x |
\/ 5 *log|----------------|
         |     ___      3 |
         \ 2*\/ 5  + 2*x  /
---------------------------
             30
5log⁡(2x3−252x3+25)30\frac{\sqrt{5} \log{\left(\frac{2 x^{3} - 2 \sqrt{5}}{2 x^{3} + 2 \sqrt{5}} \right)}}{30} 
sqrt(5)*log((-2*sqrt(5) + 2*x^3)/(2*sqrt(5) + 2*x^3))/30
Compilar la expresión [src] 
         /   3       ___\
  ___    |2*x  - 2*\/ 5 |
\/ 5 *log|--------------|
         |   3       ___|
         \2*x  + 2*\/ 5 /
-------------------------
            30
5log⁡(2x3−252x3+25)30\frac{\sqrt{5} \log{\left(\frac{2 x^{3} - 2 \sqrt{5}}{2 x^{3} + 2 \sqrt{5}} \right)}}{30} 
sqrt(5)*log((2*x^3 - 2*sqrt(5))/(2*x^3 + 2*sqrt(5)))/30
Abrimos la expresión [src] 
         /   3       ___\
  ___    |2*x  - 2*\/ 5 |
\/ 5 *log|--------------|
         |   3       ___|
         \2*x  + 2*\/ 5 /
-------------------------
            30
5log⁡(2x3−252x3+25)30\frac{\sqrt{5} \log{\left(\frac{2 x^{3} - 2 \sqrt{5}}{2 x^{3} + 2 \sqrt{5}} \right)}}{30} 
sqrt(5)*log((2*x^3 - 2*sqrt(5))/(2*x^3 + 2*sqrt(5)))/30
Potencias [src] 
         /      ___      3\
  ___    |- 2*\/ 5  + 2*x |
\/ 5 *log|----------------|
         |     ___      3 |
         \ 2*\/ 5  + 2*x  /
---------------------------
             30
5log⁡(2x3−252x3+25)30\frac{\sqrt{5} \log{\left(\frac{2 x^{3} - 2 \sqrt{5}}{2 x^{3} + 2 \sqrt{5}} \right)}}{30} 
sqrt(5)*log((-2*sqrt(5) + 2*x^3)/(2*sqrt(5) + 2*x^3))/30
Respuesta numérica [src] 
0.074535599249993*log((2*x^3 - 2*sqrt(5))/(2*x^3 + 2*sqrt(5)))
0.074535599249993*log((2*x^3 - 2*sqrt(5))/(2*x^3 + 2*sqrt(5)))
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