Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(2*x^2+4*x-1)/4-log((4*x-2*sqrt(6)+4)/(4+2*sqrt(6)+4*x))/(2*sqrt(6))
¿Cómo vas a descomponer esta log(2*x^2+4*x-1)/4-log((4*x-2*sqrt(6)+4)/(4+2*sqrt(6)+4*x))/(2*sqrt(6)) expresión en fracciones?
Solución
Ha introducido
[src]
/ ___ \
|4*x - 2*\/ 6 + 4|
log|-----------------|
/ 2 \ | ___ |
log\2*x + 4*x - 1/ \4 + 2*\/ 6 + 4*x/
------------------- - ----------------------
4 ___
2*\/ 6
$$- \frac{\log{\left(\frac{\left(4 x - 2 \sqrt{6}\right) + 4}{4 x + \left(4 + 2 \sqrt{6}\right)} \right)}}{2 \sqrt{6}} + \frac{\log{\left(\left(2 x^{2} + 4 x\right) - 1 \right)}}{4}$$
log(2*x^2 + 4*x - 1)/4 - log((4*x - 2*sqrt(6) + 4)/(4 + 2*sqrt(6) + 4*x))/(2*sqrt(6))
Simplificación general
[src]
/ ___ \
___ |2 - \/ 6 + 2*x|
\/ 6 *log|---------------|
/ 2 \ | ___ |
log\-1 + 2*x + 4*x/ \2 + \/ 6 + 2*x/
-------------------- - --------------------------
4 12
$$- \frac{\sqrt{6} \log{\left(\frac{2 x - \sqrt{6} + 2}{2 x + 2 + \sqrt{6}} \right)}}{12} + \frac{\log{\left(2 x^{2} + 4 x - 1 \right)}}{4}$$
log(-1 + 2*x^2 + 4*x)/4 - sqrt(6)*log((2 - sqrt(6) + 2*x)/(2 + sqrt(6) + 2*x))/12
Respuesta numérica
[src]
0.25*log(2*x^2 + 4*x - 1) - 0.204124145231932*log((4*x - 2*sqrt(6) + 4)/(4 + 2*sqrt(6) + 4*x))
0.25*log(2*x^2 + 4*x - 1) - 0.204124145231932*log((4*x - 2*sqrt(6) + 4)/(4 + 2*sqrt(6) + 4*x))
Parte trigonométrica
[src]
/ ___ \
___ |4 - 2*\/ 6 + 4*x|
\/ 6 *log|-----------------|
/ 2 \ | ___ |
log\-1 + 2*x + 4*x/ \4 + 2*\/ 6 + 4*x/
-------------------- - ----------------------------
4 12
$$- \frac{\sqrt{6} \log{\left(\frac{4 x - 2 \sqrt{6} + 4}{4 x + 4 + 2 \sqrt{6}} \right)}}{12} + \frac{\log{\left(2 x^{2} + 4 x - 1 \right)}}{4}$$
log(-1 + 2*x^2 + 4*x)/4 - sqrt(6)*log((4 - 2*sqrt(6) + 4*x)/(4 + 2*sqrt(6) + 4*x))/12
Combinatoria
[src]
/ ___ \
___ | 4 2*\/ 6 4*x |
\/ 6 *log|----------------- - ----------------- + -----------------|
/ 2 \ | ___ ___ ___ |
log\-1 + 2*x + 4*x/ \4 + 2*\/ 6 + 4*x 4 + 2*\/ 6 + 4*x 4 + 2*\/ 6 + 4*x/
-------------------- - --------------------------------------------------------------------
4 12
$$\frac{\log{\left(2 x^{2} + 4 x - 1 \right)}}{4} - \frac{\sqrt{6} \log{\left(\frac{4 x}{4 x + 4 + 2 \sqrt{6}} - \frac{2 \sqrt{6}}{4 x + 4 + 2 \sqrt{6}} + \frac{4}{4 x + 4 + 2 \sqrt{6}} \right)}}{12}$$
log(-1 + 2*x^2 + 4*x)/4 - sqrt(6)*log(4/(4 + 2*sqrt(6) + 4*x) - 2*sqrt(6)/(4 + 2*sqrt(6) + 4*x) + 4*x/(4 + 2*sqrt(6) + 4*x))/12
Potencias
[src]
/ ___ \
___ |4 - 2*\/ 6 + 4*x|
\/ 6 *log|-----------------|
/ 2 \ | ___ |
log\-1 + 2*x + 4*x/ \4 + 2*\/ 6 + 4*x/
-------------------- - ----------------------------
4 12
$$- \frac{\sqrt{6} \log{\left(\frac{4 x - 2 \sqrt{6} + 4}{4 x + 4 + 2 \sqrt{6}} \right)}}{12} + \frac{\log{\left(2 x^{2} + 4 x - 1 \right)}}{4}$$
log(-1 + 2*x^2 + 4*x)/4 - sqrt(6)*log((4 - 2*sqrt(6) + 4*x)/(4 + 2*sqrt(6) + 4*x))/12
Denominador racional
[src]
/ ___ \
/ 2 \ ___ | 4 2*\/ 6 4*x |
3*log\-1 + 2*x + 4*x/ - \/ 6 *log|----------------- - ----------------- + -----------------|
| ___ ___ ___ |
\4 + 2*\/ 6 + 4*x 4 + 2*\/ 6 + 4*x 4 + 2*\/ 6 + 4*x/
---------------------------------------------------------------------------------------------
12
$$\frac{3 \log{\left(2 x^{2} + 4 x - 1 \right)} - \sqrt{6} \log{\left(\frac{4 x}{4 x + \left(4 + 2 \sqrt{6}\right)} - \frac{2 \sqrt{6}}{4 x + \left(4 + 2 \sqrt{6}\right)} + \frac{4}{4 x + \left(4 + 2 \sqrt{6}\right)} \right)}}{12}$$
(3*log(-1 + 2*x^2 + 4*x) - sqrt(6)*log(4/(4 + 2*sqrt(6) + 4*x) - 2*sqrt(6)/(4 + 2*sqrt(6) + 4*x) + 4*x/(4 + 2*sqrt(6) + 4*x)))/12
Denominador común
[src]
/ ___ \
___ | 2 \/ 6 2*x |
\/ 6 *log|--------------- - --------------- + ---------------|
/ 2 \ | ___ ___ ___ |
log\-1 + 2*x + 4*x/ \2 + \/ 6 + 2*x 2 + \/ 6 + 2*x 2 + \/ 6 + 2*x/
-------------------- - --------------------------------------------------------------
4 12
$$\frac{\log{\left(2 x^{2} + 4 x - 1 \right)}}{4} - \frac{\sqrt{6} \log{\left(\frac{2 x}{2 x + 2 + \sqrt{6}} - \frac{\sqrt{6}}{2 x + 2 + \sqrt{6}} + \frac{2}{2 x + 2 + \sqrt{6}} \right)}}{12}$$
log(-1 + 2*x^2 + 4*x)/4 - sqrt(6)*log(2/(2 + sqrt(6) + 2*x) - sqrt(6)/(2 + sqrt(6) + 2*x) + 2*x/(2 + sqrt(6) + 2*x))/12
Unión de expresiones racionales
[src]
/ ___ \
___ |2 - \/ 6 + 2*x|
3*log(-1 + 2*x*(2 + x)) - \/ 6 *log|---------------|
| ___ |
\2 + \/ 6 + 2*x/
----------------------------------------------------
12
$$\frac{- \sqrt{6} \log{\left(\frac{2 x - \sqrt{6} + 2}{2 x + 2 + \sqrt{6}} \right)} + 3 \log{\left(2 x \left(x + 2\right) - 1 \right)}}{12}$$
(3*log(-1 + 2*x*(2 + x)) - sqrt(6)*log((2 - sqrt(6) + 2*x)/(2 + sqrt(6) + 2*x)))/12
Compilar la expresión
[src]
/ ___ \
___ |4*x - 2*\/ 6 + 4|
\/ 6 *log|-----------------|
/ 2 \ | ___ |
log\2*x + 4*x - 1/ \4 + 2*\/ 6 + 4*x/
------------------- - ----------------------------
4 12
$$- \frac{\sqrt{6} \log{\left(\frac{\left(4 x - 2 \sqrt{6}\right) + 4}{4 x + \left(4 + 2 \sqrt{6}\right)} \right)}}{12} + \frac{\log{\left(\left(2 x^{2} + 4 x\right) - 1 \right)}}{4}$$
log(2*x^2 + 4*x - 1)/4 - sqrt(6)*log((4*x - 2*sqrt(6) + 4)/(4 + 2*sqrt(6) + 4*x))/12