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Simplificación de expresiones/
Descomposición en fracciones simples/
log(x^2+3*x-1)/2-(3*log((2*x-sqrt(13)+3)/(2*x+sqrt(13)+3)))/(2*sqrt(13))
¿Cómo vas a descomponer esta log(x^2+3*x-1)/2-(3*log((2*x-sqrt(13)+3)/(2*x+sqrt(13)+3)))/(2*sqrt(13)) expresión en fracciones?
Solución
Ha introducido
[src]
/ ____ \
|2*x - \/ 13 + 3|
3*log|----------------|
/ 2 \ | ____ |
log\x + 3*x - 1/ \2*x + \/ 13 + 3/
----------------- - -----------------------
2 ____
2*\/ 13
$$- \frac{3 \log{\left(\frac{\left(2 x - \sqrt{13}\right) + 3}{\left(2 x + \sqrt{13}\right) + 3} \right)}}{2 \sqrt{13}} + \frac{\log{\left(\left(x^{2} + 3 x\right) - 1 \right)}}{2}$$
log(x^2 + 3*x - 1)/2 - 3*log((2*x - sqrt(13) + 3)/(2*x + sqrt(13) + 3))/(2*sqrt(13))
Simplificación general
[src]
/ ____ \
____ |3 - \/ 13 + 2*x|
3*\/ 13 *log|----------------|
/ 2 \ | ____ |
log\-1 + x + 3*x/ \3 + \/ 13 + 2*x/
------------------ - ------------------------------
2 26
$$- \frac{3 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 3}{2 x + 3 + \sqrt{13}} \right)}}{26} + \frac{\log{\left(x^{2} + 3 x - 1 \right)}}{2}$$
log(-1 + x^2 + 3*x)/2 - 3*sqrt(13)*log((3 - sqrt(13) + 2*x)/(3 + sqrt(13) + 2*x))/26
Respuesta numérica
[src]
0.5*log(x^2 + 3*x - 1) - 0.416025147168922*log((2*x - sqrt(13) + 3)/(2*x + sqrt(13) + 3))
0.5*log(x^2 + 3*x - 1) - 0.416025147168922*log((2*x - sqrt(13) + 3)/(2*x + sqrt(13) + 3))
Combinatoria
[src]
/ ____ \
____ | 3 \/ 13 2*x |
3*\/ 13 *log|---------------- - ---------------- + ----------------|
/ 2 \ | ____ ____ ____ |
log\-1 + x + 3*x/ \3 + \/ 13 + 2*x 3 + \/ 13 + 2*x 3 + \/ 13 + 2*x/
------------------ - --------------------------------------------------------------------
2 26
$$\frac{\log{\left(x^{2} + 3 x - 1 \right)}}{2} - \frac{3 \sqrt{13} \log{\left(\frac{2 x}{2 x + 3 + \sqrt{13}} - \frac{\sqrt{13}}{2 x + 3 + \sqrt{13}} + \frac{3}{2 x + 3 + \sqrt{13}} \right)}}{26}$$
log(-1 + x^2 + 3*x)/2 - 3*sqrt(13)*log(3/(3 + sqrt(13) + 2*x) - sqrt(13)/(3 + sqrt(13) + 2*x) + 2*x/(3 + sqrt(13) + 2*x))/26
Parte trigonométrica
[src]
/ ____ \
____ |3 - \/ 13 + 2*x|
3*\/ 13 *log|----------------|
/ 2 \ | ____ |
log\-1 + x + 3*x/ \3 + \/ 13 + 2*x/
------------------ - ------------------------------
2 26
$$- \frac{3 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 3}{2 x + 3 + \sqrt{13}} \right)}}{26} + \frac{\log{\left(x^{2} + 3 x - 1 \right)}}{2}$$
log(-1 + x^2 + 3*x)/2 - 3*sqrt(13)*log((3 - sqrt(13) + 2*x)/(3 + sqrt(13) + 2*x))/26
Denominador racional
[src]
/ ____ \
/ 2 \ ____ | 3 \/ 13 2*x |
13*log\-1 + x + 3*x/ - 3*\/ 13 *log|---------------- - ---------------- + ----------------|
| ____ ____ ____ |
\2*x + \/ 13 + 3 2*x + \/ 13 + 3 2*x + \/ 13 + 3/
--------------------------------------------------------------------------------------------
26
$$\frac{13 \log{\left(x^{2} + 3 x - 1 \right)} - 3 \sqrt{13} \log{\left(\frac{2 x}{\left(2 x + \sqrt{13}\right) + 3} - \frac{\sqrt{13}}{\left(2 x + \sqrt{13}\right) + 3} + \frac{3}{\left(2 x + \sqrt{13}\right) + 3} \right)}}{26}$$
(13*log(-1 + x^2 + 3*x) - 3*sqrt(13)*log(3/(2*x + sqrt(13) + 3) - sqrt(13)/(2*x + sqrt(13) + 3) + 2*x/(2*x + sqrt(13) + 3)))/26
Unión de expresiones racionales
[src]
/ ____ \
____ |3 - \/ 13 + 2*x|
13*log(-1 + x*(3 + x)) - 3*\/ 13 *log|----------------|
| ____ |
\3 + \/ 13 + 2*x/
-------------------------------------------------------
26
$$\frac{- 3 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 3}{2 x + 3 + \sqrt{13}} \right)} + 13 \log{\left(x \left(x + 3\right) - 1 \right)}}{26}$$
(13*log(-1 + x*(3 + x)) - 3*sqrt(13)*log((3 - sqrt(13) + 2*x)/(3 + sqrt(13) + 2*x)))/26
Denominador común
[src]
/ ____ \
____ | 3 \/ 13 2*x |
3*\/ 13 *log|---------------- - ---------------- + ----------------|
/ 2 \ | ____ ____ ____ |
log\-1 + x + 3*x/ \3 + \/ 13 + 2*x 3 + \/ 13 + 2*x 3 + \/ 13 + 2*x/
------------------ - --------------------------------------------------------------------
2 26
$$\frac{\log{\left(x^{2} + 3 x - 1 \right)}}{2} - \frac{3 \sqrt{13} \log{\left(\frac{2 x}{2 x + 3 + \sqrt{13}} - \frac{\sqrt{13}}{2 x + 3 + \sqrt{13}} + \frac{3}{2 x + 3 + \sqrt{13}} \right)}}{26}$$
log(-1 + x^2 + 3*x)/2 - 3*sqrt(13)*log(3/(3 + sqrt(13) + 2*x) - sqrt(13)/(3 + sqrt(13) + 2*x) + 2*x/(3 + sqrt(13) + 2*x))/26
Potencias
[src]
/ ____ \
____ |3 - \/ 13 + 2*x|
3*\/ 13 *log|----------------|
/ 2 \ | ____ |
log\-1 + x + 3*x/ \3 + \/ 13 + 2*x/
------------------ - ------------------------------
2 26
$$- \frac{3 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 3}{2 x + 3 + \sqrt{13}} \right)}}{26} + \frac{\log{\left(x^{2} + 3 x - 1 \right)}}{2}$$
log(-1 + x^2 + 3*x)/2 - 3*sqrt(13)*log((3 - sqrt(13) + 2*x)/(3 + sqrt(13) + 2*x))/26
Compilar la expresión
[src]
/ ____ \
____ |2*x - \/ 13 + 3|
3*\/ 13 *log|----------------|
/ 2 \ | ____ |
log\x + 3*x - 1/ \2*x + \/ 13 + 3/
----------------- - ------------------------------
2 26
$$- \frac{3 \sqrt{13} \log{\left(\frac{\left(2 x - \sqrt{13}\right) + 3}{\left(2 x + \sqrt{13}\right) + 3} \right)}}{26} + \frac{\log{\left(\left(x^{2} + 3 x\right) - 1 \right)}}{2}$$
log(x^2 + 3*x - 1)/2 - 3*sqrt(13)*log((2*x - sqrt(13) + 3)/(2*x + sqrt(13) + 3))/26