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Simplificación de expresiones/
Descomposición en fracciones simples/
log(sqrt(x^6+5)/(x^3+1))/6-log(sqrt(x^6+5)/(x^3-1))/6
¿Cómo vas a descomponer esta log(sqrt(x^6+5)/(x^3+1))/6-log(sqrt(x^6+5)/(x^3-1))/6 expresión en fracciones?
Solución
Ha introducido
[src]
/ ________\ / ________\
| / 6 | | / 6 |
|\/ x + 5 | |\/ x + 5 |
log|-----------| log|-----------|
| 3 | | 3 |
\ x + 1 / \ x - 1 /
---------------- - ----------------
6 6
$$- \frac{\log{\left(\frac{\sqrt{x^{6} + 5}}{x^{3} - 1} \right)}}{6} + \frac{\log{\left(\frac{\sqrt{x^{6} + 5}}{x^{3} + 1} \right)}}{6}$$
log(sqrt(x^6 + 5)/(x^3 + 1))/6 - log(sqrt(x^6 + 5)/(x^3 - 1))/6
Unión de expresiones racionales
[src]
/ ________\ / ________\
| / 6 | | / 6 |
|\/ 5 + x | |\/ 5 + x |
- log|-----------| + log|-----------|
| 3 | | 3 |
\ -1 + x / \ 1 + x /
-------------------------------------
6
$$\frac{- \log{\left(\frac{\sqrt{x^{6} + 5}}{x^{3} - 1} \right)} + \log{\left(\frac{\sqrt{x^{6} + 5}}{x^{3} + 1} \right)}}{6}$$
(-log(sqrt(5 + x^6)/(-1 + x^3)) + log(sqrt(5 + x^6)/(1 + x^3)))/6
Denominador racional
[src]
/ ________\ / ________\
| / 6 | | / 6 |
|\/ 5 + x | |\/ 5 + x |
- log|-----------| + log|-----------|
| 3 | | 3 |
\ x - 1 / \ x + 1 /
-------------------------------------
6
$$\frac{- \log{\left(\frac{\sqrt{x^{6} + 5}}{x^{3} - 1} \right)} + \log{\left(\frac{\sqrt{x^{6} + 5}}{x^{3} + 1} \right)}}{6}$$
(-log(sqrt(5 + x^6)/(x^3 - 1)) + log(sqrt(5 + x^6)/(x^3 + 1)))/6
Respuesta numérica
[src]
0.166666666666667*log(sqrt(x^6 + 5)/(x^3 + 1)) - 0.166666666666667*log(sqrt(x^6 + 5)/(x^3 - 1))
0.166666666666667*log(sqrt(x^6 + 5)/(x^3 + 1)) - 0.166666666666667*log(sqrt(x^6 + 5)/(x^3 - 1))