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Simplificación de expresiones/
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log((2*x-sqrt(41)-5)/((-5)+sqrt(41)+2*x))/sqrt(41)
¿Cómo vas a descomponer esta log((2*x-sqrt(41)-5)/((-5)+sqrt(41)+2*x))/sqrt(41) expresión en fracciones?
Solución
Ha introducido
[src]
/ ____ \
| 2*x - \/ 41 - 5|
log|-----------------|
| ____ |
\-5 + \/ 41 + 2*x/
----------------------
____
\/ 41
$$\frac{\log{\left(\frac{\left(2 x - \sqrt{41}\right) - 5}{2 x + \left(-5 + \sqrt{41}\right)} \right)}}{\sqrt{41}}$$
log((2*x - sqrt(41) - 5)/(-5 + sqrt(41) + 2*x))/sqrt(41)
Simplificación general
[src]
/ ____ \
____ |-5 - \/ 41 + 2*x|
\/ 41 *log|-----------------|
| ____ |
\-5 + \/ 41 + 2*x/
-----------------------------
41
$$\frac{\sqrt{41} \log{\left(\frac{2 x - \sqrt{41} - 5}{2 x - 5 + \sqrt{41}} \right)}}{41}$$
sqrt(41)*log((-5 - sqrt(41) + 2*x)/(-5 + sqrt(41) + 2*x))/41
Descomposición de una fracción
[src]
sqrt(41)*log(-5/(-5 + sqrt(41) + 2*x) - sqrt(41)/(-5 + sqrt(41) + 2*x) + 2*x/(-5 + sqrt(41) + 2*x))/41
$$\frac{\sqrt{41} \log{\left(\frac{2 x}{2 x + \left(-5 + \sqrt{41}\right)} - \frac{\sqrt{41}}{2 x + \left(-5 + \sqrt{41}\right)} - \frac{5}{2 x + \left(-5 + \sqrt{41}\right)} \right)}}{41}$$
/ ____ \
____ | 5 \/ 41 2*x |
\/ 41 *log|- ----------------- - ----------------- + -----------------|
| ____ ____ ____ |
\ -5 + \/ 41 + 2*x -5 + \/ 41 + 2*x -5 + \/ 41 + 2*x/
-----------------------------------------------------------------------
41
Respuesta numérica
[src]
0.156173761888606*log((2*x - sqrt(41) - 5)/(-5 + sqrt(41) + 2*x))
0.156173761888606*log((2*x - sqrt(41) - 5)/(-5 + sqrt(41) + 2*x))
Parte trigonométrica
[src]
/ ____ \
____ |-5 - \/ 41 + 2*x|
\/ 41 *log|-----------------|
| ____ |
\-5 + \/ 41 + 2*x/
-----------------------------
41
$$\frac{\sqrt{41} \log{\left(\frac{2 x - \sqrt{41} - 5}{2 x - 5 + \sqrt{41}} \right)}}{41}$$
sqrt(41)*log((-5 - sqrt(41) + 2*x)/(-5 + sqrt(41) + 2*x))/41
Denominador común
[src]
/ ____ \
____ | 5 \/ 41 2*x |
\/ 41 *log|- ----------------- - ----------------- + -----------------|
| ____ ____ ____ |
\ -5 + \/ 41 + 2*x -5 + \/ 41 + 2*x -5 + \/ 41 + 2*x/
-----------------------------------------------------------------------
41
$$\frac{\sqrt{41} \log{\left(\frac{2 x}{2 x - 5 + \sqrt{41}} - \frac{\sqrt{41}}{2 x - 5 + \sqrt{41}} - \frac{5}{2 x - 5 + \sqrt{41}} \right)}}{41}$$
sqrt(41)*log(-5/(-5 + sqrt(41) + 2*x) - sqrt(41)/(-5 + sqrt(41) + 2*x) + 2*x/(-5 + sqrt(41) + 2*x))/41
Denominador racional
[src]
/ / ____ \ \
____ |-\5 + \/ 41 - 2*x/ |
\/ 41 *log|--------------------|
| ____ |
\ -5 + \/ 41 + 2*x /
--------------------------------
41
$$\frac{\sqrt{41} \log{\left(- \frac{- 2 x + 5 + \sqrt{41}}{2 x - 5 + \sqrt{41}} \right)}}{41}$$
sqrt(41)*log(-(5 + sqrt(41) - 2*x)/(-5 + sqrt(41) + 2*x))/41
Combinatoria
[src]
/ ____ \
____ | 5 \/ 41 2*x |
\/ 41 *log|- ----------------- - ----------------- + -----------------|
| ____ ____ ____ |
\ -5 + \/ 41 + 2*x -5 + \/ 41 + 2*x -5 + \/ 41 + 2*x/
-----------------------------------------------------------------------
41
$$\frac{\sqrt{41} \log{\left(\frac{2 x}{2 x - 5 + \sqrt{41}} - \frac{\sqrt{41}}{2 x - 5 + \sqrt{41}} - \frac{5}{2 x - 5 + \sqrt{41}} \right)}}{41}$$
sqrt(41)*log(-5/(-5 + sqrt(41) + 2*x) - sqrt(41)/(-5 + sqrt(41) + 2*x) + 2*x/(-5 + sqrt(41) + 2*x))/41
Potencias
[src]
/ ____ \
____ |-5 - \/ 41 + 2*x|
\/ 41 *log|-----------------|
| ____ |
\-5 + \/ 41 + 2*x/
-----------------------------
41
$$\frac{\sqrt{41} \log{\left(\frac{2 x - \sqrt{41} - 5}{2 x - 5 + \sqrt{41}} \right)}}{41}$$
sqrt(41)*log((-5 - sqrt(41) + 2*x)/(-5 + sqrt(41) + 2*x))/41
Unión de expresiones racionales
[src]
/ ____ \
____ |-5 - \/ 41 + 2*x|
\/ 41 *log|-----------------|
| ____ |
\-5 + \/ 41 + 2*x/
-----------------------------
41
$$\frac{\sqrt{41} \log{\left(\frac{2 x - \sqrt{41} - 5}{2 x - 5 + \sqrt{41}} \right)}}{41}$$
sqrt(41)*log((-5 - sqrt(41) + 2*x)/(-5 + sqrt(41) + 2*x))/41
Compilar la expresión
[src]
/ ____ \
____ | 2*x - \/ 41 - 5|
\/ 41 *log|-----------------|
| ____ |
\-5 + \/ 41 + 2*x/
-----------------------------
41
$$\frac{\sqrt{41} \log{\left(\frac{\left(2 x - \sqrt{41}\right) - 5}{2 x + \left(-5 + \sqrt{41}\right)} \right)}}{41}$$
sqrt(41)*log((2*x - sqrt(41) - 5)/(-5 + sqrt(41) + 2*x))/41