Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log((2*x-sqrt(17)-3)/((-3)+sqrt(17)+2*x))/(2*sqrt(17))+log(x^2-3*x-2)/2
¿Cómo vas a descomponer esta log((2*x-sqrt(17)-3)/((-3)+sqrt(17)+2*x))/(2*sqrt(17))+log(x^2-3*x-2)/2 expresión en fracciones?
Solución
Ha introducido
[src]
/ ____ \
| 2*x - \/ 17 - 3|
log|-----------------|
| ____ | / 2 \
\-3 + \/ 17 + 2*x/ log\x - 3*x - 2/
---------------------- + -----------------
____ 2
2*\/ 17
$$\frac{\log{\left(\frac{\left(2 x - \sqrt{17}\right) - 3}{2 x + \left(-3 + \sqrt{17}\right)} \right)}}{2 \sqrt{17}} + \frac{\log{\left(\left(x^{2} - 3 x\right) - 2 \right)}}{2}$$
log((2*x - sqrt(17) - 3)/(-3 + sqrt(17) + 2*x))/((2*sqrt(17))) + log(x^2 - 3*x - 2)/2
Simplificación general
[src]
/ ____ \
____ |-3 - \/ 17 + 2*x|
\/ 17 *log|-----------------|
/ 2 \ | ____ |
log\-2 + x - 3*x/ \-3 + \/ 17 + 2*x/
------------------ + -----------------------------
2 34
$$\frac{\sqrt{17} \log{\left(\frac{2 x - \sqrt{17} - 3}{2 x - 3 + \sqrt{17}} \right)}}{34} + \frac{\log{\left(x^{2} - 3 x - 2 \right)}}{2}$$
log(-2 + x^2 - 3*x)/2 + sqrt(17)*log((-3 - sqrt(17) + 2*x)/(-3 + sqrt(17) + 2*x))/34
Respuesta numérica
[src]
0.5*log(x^2 - 3*x - 2) + 0.121267812518166*log((2*x - sqrt(17) - 3)/(-3 + sqrt(17) + 2*x))
0.5*log(x^2 - 3*x - 2) + 0.121267812518166*log((2*x - sqrt(17) - 3)/(-3 + sqrt(17) + 2*x))
Denominador racional
[src]
/ ____ \
/ 2 \ ____ | 3 \/ 17 2*x |
17*log\-2 + x - 3*x/ + \/ 17 *log|- ----------------- - ----------------- + -----------------|
| ____ ____ ____ |
\ -3 + \/ 17 + 2*x -3 + \/ 17 + 2*x -3 + \/ 17 + 2*x/
-----------------------------------------------------------------------------------------------
34
$$\frac{17 \log{\left(x^{2} - 3 x - 2 \right)} + \sqrt{17} \log{\left(\frac{2 x}{2 x - 3 + \sqrt{17}} - \frac{\sqrt{17}}{2 x - 3 + \sqrt{17}} - \frac{3}{2 x - 3 + \sqrt{17}} \right)}}{34}$$
(17*log(-2 + x^2 - 3*x) + sqrt(17)*log(-3/(-3 + sqrt(17) + 2*x) - sqrt(17)/(-3 + sqrt(17) + 2*x) + 2*x/(-3 + sqrt(17) + 2*x)))/34
Combinatoria
[src]
/ ____ \
____ | 3 \/ 17 2*x |
\/ 17 *log|- ----------------- - ----------------- + -----------------|
/ 2 \ | ____ ____ ____ |
log\-2 + x - 3*x/ \ -3 + \/ 17 + 2*x -3 + \/ 17 + 2*x -3 + \/ 17 + 2*x/
------------------ + -----------------------------------------------------------------------
2 34
$$\frac{\log{\left(x^{2} - 3 x - 2 \right)}}{2} + \frac{\sqrt{17} \log{\left(\frac{2 x}{2 x - 3 + \sqrt{17}} - \frac{\sqrt{17}}{2 x - 3 + \sqrt{17}} - \frac{3}{2 x - 3 + \sqrt{17}} \right)}}{34}$$
log(-2 + x^2 - 3*x)/2 + sqrt(17)*log(-3/(-3 + sqrt(17) + 2*x) - sqrt(17)/(-3 + sqrt(17) + 2*x) + 2*x/(-3 + sqrt(17) + 2*x))/34
Unión de expresiones racionales
[src]
/ ____ \
____ |-3 - \/ 17 + 2*x|
17*log(-2 + x*(-3 + x)) + \/ 17 *log|-----------------|
| ____ |
\-3 + \/ 17 + 2*x/
-------------------------------------------------------
34
$$\frac{\sqrt{17} \log{\left(\frac{2 x - \sqrt{17} - 3}{2 x - 3 + \sqrt{17}} \right)} + 17 \log{\left(x \left(x - 3\right) - 2 \right)}}{34}$$
(17*log(-2 + x*(-3 + x)) + sqrt(17)*log((-3 - sqrt(17) + 2*x)/(-3 + sqrt(17) + 2*x)))/34
Potencias
[src]
/ ____ \
____ |-3 - \/ 17 + 2*x|
\/ 17 *log|-----------------|
/ 2 \ | ____ |
log\-2 + x - 3*x/ \-3 + \/ 17 + 2*x/
------------------ + -----------------------------
2 34
$$\frac{\sqrt{17} \log{\left(\frac{2 x - \sqrt{17} - 3}{2 x - 3 + \sqrt{17}} \right)}}{34} + \frac{\log{\left(x^{2} - 3 x - 2 \right)}}{2}$$
log(-2 + x^2 - 3*x)/2 + sqrt(17)*log((-3 - sqrt(17) + 2*x)/(-3 + sqrt(17) + 2*x))/34
Parte trigonométrica
[src]
/ ____ \
____ |-3 - \/ 17 + 2*x|
\/ 17 *log|-----------------|
/ 2 \ | ____ |
log\-2 + x - 3*x/ \-3 + \/ 17 + 2*x/
------------------ + -----------------------------
2 34
$$\frac{\sqrt{17} \log{\left(\frac{2 x - \sqrt{17} - 3}{2 x - 3 + \sqrt{17}} \right)}}{34} + \frac{\log{\left(x^{2} - 3 x - 2 \right)}}{2}$$
log(-2 + x^2 - 3*x)/2 + sqrt(17)*log((-3 - sqrt(17) + 2*x)/(-3 + sqrt(17) + 2*x))/34
Compilar la expresión
[src]
/ ____ \
____ | 2*x - \/ 17 - 3|
\/ 17 *log|-----------------|
/ 2 \ | ____ |
log\x - 3*x - 2/ \-3 + \/ 17 + 2*x/
----------------- + -----------------------------
2 34
$$\frac{\sqrt{17} \log{\left(\frac{\left(2 x - \sqrt{17}\right) - 3}{2 x + \left(-3 + \sqrt{17}\right)} \right)}}{34} + \frac{\log{\left(\left(x^{2} - 3 x\right) - 2 \right)}}{2}$$
log(x^2 - 3*x - 2)/2 + sqrt(17)*log((2*x - sqrt(17) - 3)/(-3 + sqrt(17) + 2*x))/34
Denominador común
[src]
/ ____ \
____ | 3 \/ 17 2*x |
\/ 17 *log|- ----------------- - ----------------- + -----------------|
/ 2 \ | ____ ____ ____ |
log\-2 + x - 3*x/ \ -3 + \/ 17 + 2*x -3 + \/ 17 + 2*x -3 + \/ 17 + 2*x/
------------------ + -----------------------------------------------------------------------
2 34
$$\frac{\log{\left(x^{2} - 3 x - 2 \right)}}{2} + \frac{\sqrt{17} \log{\left(\frac{2 x}{2 x - 3 + \sqrt{17}} - \frac{\sqrt{17}}{2 x - 3 + \sqrt{17}} - \frac{3}{2 x - 3 + \sqrt{17}} \right)}}{34}$$
log(-2 + x^2 - 3*x)/2 + sqrt(17)*log(-3/(-3 + sqrt(17) + 2*x) - sqrt(17)/(-3 + sqrt(17) + 2*x) + 2*x/(-3 + sqrt(17) + 2*x))/34