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Simplificación de expresiones/
Descomposición en fracciones simples/
log(sqrt(x^8+1)/(x^4+1))/8-log(sqrt(x^8+1)/(x^4-1))/8
¿Cómo vas a descomponer esta log(sqrt(x^8+1)/(x^4+1))/8-log(sqrt(x^8+1)/(x^4-1))/8 expresión en fracciones?
Solución
Ha introducido
[src]
/ ________\ / ________\
| / 8 | | / 8 |
|\/ x + 1 | |\/ x + 1 |
log|-----------| log|-----------|
| 4 | | 4 |
\ x + 1 / \ x - 1 /
---------------- - ----------------
8 8
$$- \frac{\log{\left(\frac{\sqrt{x^{8} + 1}}{x^{4} - 1} \right)}}{8} + \frac{\log{\left(\frac{\sqrt{x^{8} + 1}}{x^{4} + 1} \right)}}{8}$$
log(sqrt(x^8 + 1)/(x^4 + 1))/8 - log(sqrt(x^8 + 1)/(x^4 - 1))/8
Respuesta numérica
[src]
0.125*log(sqrt(x^8 + 1)/(x^4 + 1)) - 0.125*log(sqrt(x^8 + 1)/(x^4 - 1))
0.125*log(sqrt(x^8 + 1)/(x^4 + 1)) - 0.125*log(sqrt(x^8 + 1)/(x^4 - 1))
Denominador racional
[src]
/ ________\ / ________\
| / 8 | | / 8 |
|\/ 1 + x | |\/ 1 + x |
- log|-----------| + log|-----------|
| 4 | | 4 |
\ x - 1 / \ x + 1 /
-------------------------------------
8
$$\frac{- \log{\left(\frac{\sqrt{x^{8} + 1}}{x^{4} - 1} \right)} + \log{\left(\frac{\sqrt{x^{8} + 1}}{x^{4} + 1} \right)}}{8}$$
(-log(sqrt(1 + x^8)/(x^4 - 1)) + log(sqrt(1 + x^8)/(x^4 + 1)))/8
Unión de expresiones racionales
[src]
/ ________\ / ________\
| / 8 | | / 8 |
|\/ 1 + x | |\/ 1 + x |
- log|-----------| + log|-----------|
| 4 | | 4 |
\ -1 + x / \ 1 + x /
-------------------------------------
8
$$\frac{- \log{\left(\frac{\sqrt{x^{8} + 1}}{x^{4} - 1} \right)} + \log{\left(\frac{\sqrt{x^{8} + 1}}{x^{4} + 1} \right)}}{8}$$
(-log(sqrt(1 + x^8)/(-1 + x^4)) + log(sqrt(1 + x^8)/(1 + x^4)))/8