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Simplificación de expresiones/
Descomposición en fracciones simples/
log((2*t-2^(3/2))/(2^(3/2)+2*t))/2^(3/2)
¿Cómo vas a descomponer esta log((2*t-2^(3/2))/(2^(3/2)+2*t))/2^(3/2) expresión en fracciones?
Solución
Ha introducido
[src]
/ 3/2\
|2*t - 2 |
log|----------|
| 3/2 |
\2 + 2*t/
---------------
3/2
2
$$\frac{\log{\left(\frac{2 t - 2^{\frac{3}{2}}}{2 t + 2^{\frac{3}{2}}} \right)}}{2^{\frac{3}{2}}}$$
log((2*t - 2^(3/2))/(2^(3/2) + 2*t))/2^(3/2)
Descomposición de una fracción
[src]
sqrt(2)*log(-2*sqrt(2)/(2*t + 2*sqrt(2)) + 2*t/(2*t + 2*sqrt(2)))/4
$$\frac{\sqrt{2} \log{\left(\frac{2 t}{2 t + 2 \sqrt{2}} - \frac{2 \sqrt{2}}{2 t + 2 \sqrt{2}} \right)}}{4}$$
/ ___ \
___ | 2*\/ 2 2*t |
\/ 2 *log|- ------------- + -------------|
| ___ ___|
\ 2*t + 2*\/ 2 2*t + 2*\/ 2 /
------------------------------------------
4
Simplificación general
[src]
/ ___\
___ |t - \/ 2 |
\/ 2 *log|---------|
| ___|
\t + \/ 2 /
--------------------
4
$$\frac{\sqrt{2} \log{\left(\frac{t - \sqrt{2}}{t + \sqrt{2}} \right)}}{4}$$
sqrt(2)*log((t - sqrt(2))/(t + sqrt(2)))/4
Respuesta numérica
[src]
0.353553390593274*log((2*t - 2^(3/2))/(2^(3/2) + 2*t))
0.353553390593274*log((2*t - 2^(3/2))/(2^(3/2) + 2*t))
Denominador común
[src]
/ ___ \
___ | t \/ 2 |
\/ 2 *log|--------- - ---------|
| ___ ___|
\t + \/ 2 t + \/ 2 /
--------------------------------
4
$$\frac{\sqrt{2} \log{\left(\frac{t}{t + \sqrt{2}} - \frac{\sqrt{2}}{t + \sqrt{2}} \right)}}{4}$$
sqrt(2)*log(t/(t + sqrt(2)) - sqrt(2)/(t + sqrt(2)))/4
Parte trigonométrica
[src]
/ ___ \
___ |- 2*\/ 2 + 2*t|
\/ 2 *log|---------------|
| ___ |
\ 2*t + 2*\/ 2 /
--------------------------
4
$$\frac{\sqrt{2} \log{\left(\frac{2 t - 2 \sqrt{2}}{2 t + 2 \sqrt{2}} \right)}}{4}$$
sqrt(2)*log((-2*sqrt(2) + 2*t)/(2*t + 2*sqrt(2)))/4
Denominador racional
[src]
/ 2 ___\
___ |2 + t - 2*t*\/ 2 |
\/ 2 *log|------------------|
| 2 |
\ -2 + t /
-----------------------------
4
$$\frac{\sqrt{2} \log{\left(\frac{t^{2} - 2 \sqrt{2} t + 2}{t^{2} - 2} \right)}}{4}$$
sqrt(2)*log((2 + t^2 - 2*t*sqrt(2))/(-2 + t^2))/4
Potencias
[src]
/ ___ \
___ |- 2*\/ 2 + 2*t|
\/ 2 *log|---------------|
| ___ |
\ 2*t + 2*\/ 2 /
--------------------------
4
$$\frac{\sqrt{2} \log{\left(\frac{2 t - 2 \sqrt{2}}{2 t + 2 \sqrt{2}} \right)}}{4}$$
sqrt(2)*log((-2*sqrt(2) + 2*t)/(2*t + 2*sqrt(2)))/4
Combinatoria
[src]
/ ___ \
___ | 2*\/ 2 2*t |
\/ 2 *log|- ------------- + -------------|
| ___ ___|
\ 2*t + 2*\/ 2 2*t + 2*\/ 2 /
------------------------------------------
4
$$\frac{\sqrt{2} \log{\left(\frac{2 t}{2 t + 2 \sqrt{2}} - \frac{2 \sqrt{2}}{2 t + 2 \sqrt{2}} \right)}}{4}$$
sqrt(2)*log(-2*sqrt(2)/(2*t + 2*sqrt(2)) + 2*t/(2*t + 2*sqrt(2)))/4
Unión de expresiones racionales
[src]
/ ___\
___ |t - \/ 2 |
\/ 2 *log|---------|
| ___|
\t + \/ 2 /
--------------------
4
$$\frac{\sqrt{2} \log{\left(\frac{t - \sqrt{2}}{t + \sqrt{2}} \right)}}{4}$$
sqrt(2)*log((t - sqrt(2))/(t + sqrt(2)))/4
Compilar la expresión
[src]
/ 3/2\
___ |2*t - 2 |
\/ 2 *log|----------|
| 3/2 |
\2 + 2*t/
---------------------
4
$$\frac{\sqrt{2} \log{\left(\frac{2 t - 2^{\frac{3}{2}}}{2 t + 2^{\frac{3}{2}}} \right)}}{4}$$
sqrt(2)*log((2*t - 2^(3/2))/(2^(3/2) + 2*t))/4