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Simplificación de expresiones/
Descomposición en fracciones simples/
log((2*x^4-2^(3/2))/(2^(3/2)+2*x^4))/2^(7/2)
¿Cómo vas a descomponer esta log((2*x^4-2^(3/2))/(2^(3/2)+2*x^4))/2^(7/2) expresión en fracciones?
Solución
Ha introducido
[src]
/ 4 3/2\
|2*x - 2 |
log|-----------|
| 3/2 4|
\2 + 2*x /
----------------
7/2
2
$$\frac{\log{\left(\frac{2 x^{4} - 2^{\frac{3}{2}}}{2 x^{4} + 2^{\frac{3}{2}}} \right)}}{2^{\frac{7}{2}}}$$
log((2*x^4 - 2^(3/2))/(2^(3/2) + 2*x^4))/2^(7/2)
Simplificación general
[src]
/ 4 ___\
___ |x - \/ 2 |
\/ 2 *log|----------|
| ___ 4|
\\/ 2 + x /
---------------------
16
$$\frac{\sqrt{2} \log{\left(\frac{x^{4} - \sqrt{2}}{x^{4} + \sqrt{2}} \right)}}{16}$$
sqrt(2)*log((x^4 - sqrt(2))/(sqrt(2) + x^4))/16
Descomposición de una fracción
[src]
sqrt(2)*log(-2*sqrt(2)/(2*sqrt(2) + 2*x^4) + 2*x^4/(2*sqrt(2) + 2*x^4))/16
$$\frac{\sqrt{2} \log{\left(\frac{2 x^{4}}{2 x^{4} + 2 \sqrt{2}} - \frac{2 \sqrt{2}}{2 x^{4} + 2 \sqrt{2}} \right)}}{16}$$
/ ___ 4 \
___ | 2*\/ 2 2*x |
\/ 2 *log|- -------------- + --------------|
| ___ 4 ___ 4|
\ 2*\/ 2 + 2*x 2*\/ 2 + 2*x /
--------------------------------------------
16
Respuesta numérica
[src]
0.0883883476483184*log((2*x^4 - 2^(3/2))/(2^(3/2) + 2*x^4))
0.0883883476483184*log((2*x^4 - 2^(3/2))/(2^(3/2) + 2*x^4))
Parte trigonométrica
[src]
/ ___ 4\
___ |- 2*\/ 2 + 2*x |
\/ 2 *log|----------------|
| ___ 4 |
\ 2*\/ 2 + 2*x /
---------------------------
16
$$\frac{\sqrt{2} \log{\left(\frac{2 x^{4} - 2 \sqrt{2}}{2 x^{4} + 2 \sqrt{2}} \right)}}{16}$$
sqrt(2)*log((-2*sqrt(2) + 2*x^4)/(2*sqrt(2) + 2*x^4))/16
Denominador racional
[src]
/ 8 ___ 4\
___ |2 + x - 2*\/ 2 *x |
\/ 2 *log|-------------------|
| 8 |
\ -2 + x /
------------------------------
16
$$\frac{\sqrt{2} \log{\left(\frac{x^{8} - 2 \sqrt{2} x^{4} + 2}{x^{8} - 2} \right)}}{16}$$
sqrt(2)*log((2 + x^8 - 2*sqrt(2)*x^4)/(-2 + x^8))/16
Combinatoria
[src]
/ ___ 4 \
___ | 2*\/ 2 2*x |
\/ 2 *log|- -------------- + --------------|
| ___ 4 ___ 4|
\ 2*\/ 2 + 2*x 2*\/ 2 + 2*x /
--------------------------------------------
16
$$\frac{\sqrt{2} \log{\left(\frac{2 x^{4}}{2 x^{4} + 2 \sqrt{2}} - \frac{2 \sqrt{2}}{2 x^{4} + 2 \sqrt{2}} \right)}}{16}$$
sqrt(2)*log(-2*sqrt(2)/(2*sqrt(2) + 2*x^4) + 2*x^4/(2*sqrt(2) + 2*x^4))/16
Potencias
[src]
/ ___ 4\
___ |- 2*\/ 2 + 2*x |
\/ 2 *log|----------------|
| ___ 4 |
\ 2*\/ 2 + 2*x /
---------------------------
16
$$\frac{\sqrt{2} \log{\left(\frac{2 x^{4} - 2 \sqrt{2}}{2 x^{4} + 2 \sqrt{2}} \right)}}{16}$$
sqrt(2)*log((-2*sqrt(2) + 2*x^4)/(2*sqrt(2) + 2*x^4))/16
Unión de expresiones racionales
[src]
/ 4 ___\
___ |x - \/ 2 |
\/ 2 *log|----------|
| ___ 4|
\\/ 2 + x /
---------------------
16
$$\frac{\sqrt{2} \log{\left(\frac{x^{4} - \sqrt{2}}{x^{4} + \sqrt{2}} \right)}}{16}$$
sqrt(2)*log((x^4 - sqrt(2))/(sqrt(2) + x^4))/16
Denominador común
[src]
/ 4 ___ \
___ | x \/ 2 |
\/ 2 *log|---------- - ----------|
| ___ 4 ___ 4|
\\/ 2 + x \/ 2 + x /
----------------------------------
16
$$\frac{\sqrt{2} \log{\left(\frac{x^{4}}{x^{4} + \sqrt{2}} - \frac{\sqrt{2}}{x^{4} + \sqrt{2}} \right)}}{16}$$
sqrt(2)*log(x^4/(sqrt(2) + x^4) - sqrt(2)/(sqrt(2) + x^4))/16
Compilar la expresión
[src]
/ 4 3/2\
___ |2*x - 2 |
\/ 2 *log|-----------|
| 3/2 4|
\2 + 2*x /
----------------------
16
$$\frac{\sqrt{2} \log{\left(\frac{2 x^{4} - 2^{\frac{3}{2}}}{2 x^{4} + 2^{\frac{3}{2}}} \right)}}{16}$$
sqrt(2)*log((2*x^4 - 2^(3/2))/(2^(3/2) + 2*x^4))/16