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Simplificación de expresiones/
Descomposición en fracciones simples/
log(x^2+5*x+3)/2-(5*log((2*x-sqrt(13)+5)/(5+sqrt(13)+2*x)))/(2*sqrt(13))
¿Cómo vas a descomponer esta log(x^2+5*x+3)/2-(5*log((2*x-sqrt(13)+5)/(5+sqrt(13)+2*x)))/(2*sqrt(13)) expresión en fracciones?
Solución
Ha introducido
[src]
/ ____ \
|2*x - \/ 13 + 5|
5*log|----------------|
/ 2 \ | ____ |
log\x + 5*x + 3/ \5 + \/ 13 + 2*x/
----------------- - -----------------------
2 ____
2*\/ 13
$$- \frac{5 \log{\left(\frac{\left(2 x - \sqrt{13}\right) + 5}{2 x + \left(\sqrt{13} + 5\right)} \right)}}{2 \sqrt{13}} + \frac{\log{\left(\left(x^{2} + 5 x\right) + 3 \right)}}{2}$$
log(x^2 + 5*x + 3)/2 - 5*log((2*x - sqrt(13) + 5)/(5 + sqrt(13) + 2*x))/(2*sqrt(13))
Simplificación general
[src]
/ ____ \
____ |5 - \/ 13 + 2*x|
5*\/ 13 *log|----------------|
/ 2 \ | ____ |
log\3 + x + 5*x/ \5 + \/ 13 + 2*x/
----------------- - ------------------------------
2 26
$$- \frac{5 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 5}{2 x + \sqrt{13} + 5} \right)}}{26} + \frac{\log{\left(x^{2} + 5 x + 3 \right)}}{2}$$
log(3 + x^2 + 5*x)/2 - 5*sqrt(13)*log((5 - sqrt(13) + 2*x)/(5 + sqrt(13) + 2*x))/26
Combinatoria
[src]
/ ____ \
____ | 5 \/ 13 2*x |
5*\/ 13 *log|---------------- - ---------------- + ----------------|
/ 2 \ | ____ ____ ____ |
log\3 + x + 5*x/ \5 + \/ 13 + 2*x 5 + \/ 13 + 2*x 5 + \/ 13 + 2*x/
----------------- - --------------------------------------------------------------------
2 26
$$\frac{\log{\left(x^{2} + 5 x + 3 \right)}}{2} - \frac{5 \sqrt{13} \log{\left(\frac{2 x}{2 x + \sqrt{13} + 5} - \frac{\sqrt{13}}{2 x + \sqrt{13} + 5} + \frac{5}{2 x + \sqrt{13} + 5} \right)}}{26}$$
log(3 + x^2 + 5*x)/2 - 5*sqrt(13)*log(5/(5 + sqrt(13) + 2*x) - sqrt(13)/(5 + sqrt(13) + 2*x) + 2*x/(5 + sqrt(13) + 2*x))/26
Denominador racional
[src]
/ ____ \
/ 2 \ ____ | 5 \/ 13 2*x |
13*log\3 + x + 5*x/ - 5*\/ 13 *log|---------------- - ---------------- + ----------------|
| ____ ____ ____ |
\5 + \/ 13 + 2*x 5 + \/ 13 + 2*x 5 + \/ 13 + 2*x/
-------------------------------------------------------------------------------------------
26
$$\frac{13 \log{\left(x^{2} + 5 x + 3 \right)} - 5 \sqrt{13} \log{\left(\frac{2 x}{2 x + \left(\sqrt{13} + 5\right)} - \frac{\sqrt{13}}{2 x + \left(\sqrt{13} + 5\right)} + \frac{5}{2 x + \left(\sqrt{13} + 5\right)} \right)}}{26}$$
(13*log(3 + x^2 + 5*x) - 5*sqrt(13)*log(5/(5 + sqrt(13) + 2*x) - sqrt(13)/(5 + sqrt(13) + 2*x) + 2*x/(5 + sqrt(13) + 2*x)))/26
Respuesta numérica
[src]
0.5*log(x^2 + 5*x + 3) - 0.693375245281536*log((2*x - sqrt(13) + 5)/(5 + sqrt(13) + 2*x))
0.5*log(x^2 + 5*x + 3) - 0.693375245281536*log((2*x - sqrt(13) + 5)/(5 + sqrt(13) + 2*x))
Denominador común
[src]
/ ____ \
____ | 5 \/ 13 2*x |
5*\/ 13 *log|---------------- - ---------------- + ----------------|
/ 2 \ | ____ ____ ____ |
log\3 + x + 5*x/ \5 + \/ 13 + 2*x 5 + \/ 13 + 2*x 5 + \/ 13 + 2*x/
----------------- - --------------------------------------------------------------------
2 26
$$\frac{\log{\left(x^{2} + 5 x + 3 \right)}}{2} - \frac{5 \sqrt{13} \log{\left(\frac{2 x}{2 x + \sqrt{13} + 5} - \frac{\sqrt{13}}{2 x + \sqrt{13} + 5} + \frac{5}{2 x + \sqrt{13} + 5} \right)}}{26}$$
log(3 + x^2 + 5*x)/2 - 5*sqrt(13)*log(5/(5 + sqrt(13) + 2*x) - sqrt(13)/(5 + sqrt(13) + 2*x) + 2*x/(5 + sqrt(13) + 2*x))/26
Unión de expresiones racionales
[src]
/ ____ \
____ |5 - \/ 13 + 2*x|
13*log(3 + x*(5 + x)) - 5*\/ 13 *log|----------------|
| ____ |
\5 + \/ 13 + 2*x/
------------------------------------------------------
26
$$\frac{- 5 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 5}{2 x + \sqrt{13} + 5} \right)} + 13 \log{\left(x \left(x + 5\right) + 3 \right)}}{26}$$
(13*log(3 + x*(5 + x)) - 5*sqrt(13)*log((5 - sqrt(13) + 2*x)/(5 + sqrt(13) + 2*x)))/26
Potencias
[src]
/ ____ \
____ |5 - \/ 13 + 2*x|
5*\/ 13 *log|----------------|
/ 2 \ | ____ |
log\3 + x + 5*x/ \5 + \/ 13 + 2*x/
----------------- - ------------------------------
2 26
$$- \frac{5 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 5}{2 x + \sqrt{13} + 5} \right)}}{26} + \frac{\log{\left(x^{2} + 5 x + 3 \right)}}{2}$$
log(3 + x^2 + 5*x)/2 - 5*sqrt(13)*log((5 - sqrt(13) + 2*x)/(5 + sqrt(13) + 2*x))/26
Parte trigonométrica
[src]
/ ____ \
____ |5 - \/ 13 + 2*x|
5*\/ 13 *log|----------------|
/ 2 \ | ____ |
log\3 + x + 5*x/ \5 + \/ 13 + 2*x/
----------------- - ------------------------------
2 26
$$- \frac{5 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 5}{2 x + \sqrt{13} + 5} \right)}}{26} + \frac{\log{\left(x^{2} + 5 x + 3 \right)}}{2}$$
log(3 + x^2 + 5*x)/2 - 5*sqrt(13)*log((5 - sqrt(13) + 2*x)/(5 + sqrt(13) + 2*x))/26
Compilar la expresión
[src]
/ ____ \
____ |2*x - \/ 13 + 5|
5*\/ 13 *log|----------------|
/ 2 \ | ____ |
log\x + 5*x + 3/ \5 + \/ 13 + 2*x/
----------------- - ------------------------------
2 26
$$- \frac{5 \sqrt{13} \log{\left(\frac{\left(2 x - \sqrt{13}\right) + 5}{2 x + \left(\sqrt{13} + 5\right)} \right)}}{26} + \frac{\log{\left(\left(x^{2} + 5 x\right) + 3 \right)}}{2}$$
log(x^2 + 5*x + 3)/2 - 5*sqrt(13)*log((2*x - sqrt(13) + 5)/(5 + sqrt(13) + 2*x))/26