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log((6*x-sqrt(37)+5)/(5+sqrt(37)+6*x))/sqrt(37)
¿Cómo vas a descomponer esta log((6*x-sqrt(37)+5)/(5+sqrt(37)+6*x))/sqrt(37) expresión en fracciones?
Solución
Ha introducido
[src]
/ ____ \
|6*x - \/ 37 + 5|
log|----------------|
| ____ |
\5 + \/ 37 + 6*x/
---------------------
____
\/ 37
$$\frac{\log{\left(\frac{\left(6 x - \sqrt{37}\right) + 5}{6 x + \left(5 + \sqrt{37}\right)} \right)}}{\sqrt{37}}$$
log((6*x - sqrt(37) + 5)/(5 + sqrt(37) + 6*x))/sqrt(37)
Descomposición de una fracción
[src]
sqrt(37)*log(5/(5 + sqrt(37) + 6*x) - sqrt(37)/(5 + sqrt(37) + 6*x) + 6*x/(5 + sqrt(37) + 6*x))/37
$$\frac{\sqrt{37} \log{\left(\frac{6 x}{6 x + \left(5 + \sqrt{37}\right)} - \frac{\sqrt{37}}{6 x + \left(5 + \sqrt{37}\right)} + \frac{5}{6 x + \left(5 + \sqrt{37}\right)} \right)}}{37}$$
/ ____ \
____ | 5 \/ 37 6*x |
\/ 37 *log|---------------- - ---------------- + ----------------|
| ____ ____ ____ |
\5 + \/ 37 + 6*x 5 + \/ 37 + 6*x 5 + \/ 37 + 6*x/
------------------------------------------------------------------
37
Simplificación general
[src]
/ ____ \
____ |5 - \/ 37 + 6*x|
\/ 37 *log|----------------|
| ____ |
\5 + \/ 37 + 6*x/
----------------------------
37
$$\frac{\sqrt{37} \log{\left(\frac{6 x - \sqrt{37} + 5}{6 x + 5 + \sqrt{37}} \right)}}{37}$$
sqrt(37)*log((5 - sqrt(37) + 6*x)/(5 + sqrt(37) + 6*x))/37
Respuesta numérica
[src]
0.164398987305357*log((6*x - sqrt(37) + 5)/(5 + sqrt(37) + 6*x))
0.164398987305357*log((6*x - sqrt(37) + 5)/(5 + sqrt(37) + 6*x))
Unión de expresiones racionales
[src]
/ ____ \
____ |5 - \/ 37 + 6*x|
\/ 37 *log|----------------|
| ____ |
\5 + \/ 37 + 6*x/
----------------------------
37
$$\frac{\sqrt{37} \log{\left(\frac{6 x - \sqrt{37} + 5}{6 x + 5 + \sqrt{37}} \right)}}{37}$$
sqrt(37)*log((5 - sqrt(37) + 6*x)/(5 + sqrt(37) + 6*x))/37
Combinatoria
[src]
/ ____ \
____ | 5 \/ 37 6*x |
\/ 37 *log|---------------- - ---------------- + ----------------|
| ____ ____ ____ |
\5 + \/ 37 + 6*x 5 + \/ 37 + 6*x 5 + \/ 37 + 6*x/
------------------------------------------------------------------
37
$$\frac{\sqrt{37} \log{\left(\frac{6 x}{6 x + 5 + \sqrt{37}} - \frac{\sqrt{37}}{6 x + 5 + \sqrt{37}} + \frac{5}{6 x + 5 + \sqrt{37}} \right)}}{37}$$
sqrt(37)*log(5/(5 + sqrt(37) + 6*x) - sqrt(37)/(5 + sqrt(37) + 6*x) + 6*x/(5 + sqrt(37) + 6*x))/37
Denominador común
[src]
/ ____ \
____ | 5 \/ 37 6*x |
\/ 37 *log|---------------- - ---------------- + ----------------|
| ____ ____ ____ |
\5 + \/ 37 + 6*x 5 + \/ 37 + 6*x 5 + \/ 37 + 6*x/
------------------------------------------------------------------
37
$$\frac{\sqrt{37} \log{\left(\frac{6 x}{6 x + 5 + \sqrt{37}} - \frac{\sqrt{37}}{6 x + 5 + \sqrt{37}} + \frac{5}{6 x + 5 + \sqrt{37}} \right)}}{37}$$
sqrt(37)*log(5/(5 + sqrt(37) + 6*x) - sqrt(37)/(5 + sqrt(37) + 6*x) + 6*x/(5 + sqrt(37) + 6*x))/37
Denominador racional
[src]
/ ____ \
____ |5 - \/ 37 + 6*x|
\/ 37 *log|----------------|
| ____ |
\5 + \/ 37 + 6*x/
----------------------------
37
$$\frac{\sqrt{37} \log{\left(\frac{6 x - \sqrt{37} + 5}{6 x + \left(5 + \sqrt{37}\right)} \right)}}{37}$$
sqrt(37)*log((5 - sqrt(37) + 6*x)/(5 + sqrt(37) + 6*x))/37
Parte trigonométrica
[src]
/ ____ \
____ |5 - \/ 37 + 6*x|
\/ 37 *log|----------------|
| ____ |
\5 + \/ 37 + 6*x/
----------------------------
37
$$\frac{\sqrt{37} \log{\left(\frac{6 x - \sqrt{37} + 5}{6 x + 5 + \sqrt{37}} \right)}}{37}$$
sqrt(37)*log((5 - sqrt(37) + 6*x)/(5 + sqrt(37) + 6*x))/37
Potencias
[src]
/ ____ \
____ |5 - \/ 37 + 6*x|
\/ 37 *log|----------------|
| ____ |
\5 + \/ 37 + 6*x/
----------------------------
37
$$\frac{\sqrt{37} \log{\left(\frac{6 x - \sqrt{37} + 5}{6 x + 5 + \sqrt{37}} \right)}}{37}$$
sqrt(37)*log((5 - sqrt(37) + 6*x)/(5 + sqrt(37) + 6*x))/37
Compilar la expresión
[src]
/ ____ \
____ |6*x - \/ 37 + 5|
\/ 37 *log|----------------|
| ____ |
\5 + \/ 37 + 6*x/
----------------------------
37
$$\frac{\sqrt{37} \log{\left(\frac{\left(6 x - \sqrt{37}\right) + 5}{6 x + \left(5 + \sqrt{37}\right)} \right)}}{37}$$
sqrt(37)*log((6*x - sqrt(37) + 5)/(5 + sqrt(37) + 6*x))/37