Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(x^2+6*x+4)/2-(3*log((2*x-2*sqrt(5)+6)/(2*x+2*sqrt(5)+6)))/(2*sqrt(5))
¿Cómo vas a descomponer esta log(x^2+6*x+4)/2-(3*log((2*x-2*sqrt(5)+6)/(2*x+2*sqrt(5)+6)))/(2*sqrt(5)) expresión en fracciones?
Solución
Ha introducido
[src]
/ ___ \
|2*x - 2*\/ 5 + 6|
3*log|-----------------|
/ 2 \ | ___ |
log\x + 6*x + 4/ \2*x + 2*\/ 5 + 6/
----------------- - ------------------------
2 ___
2*\/ 5
$$- \frac{3 \log{\left(\frac{\left(2 x - 2 \sqrt{5}\right) + 6}{\left(2 x + 2 \sqrt{5}\right) + 6} \right)}}{2 \sqrt{5}} + \frac{\log{\left(\left(x^{2} + 6 x\right) + 4 \right)}}{2}$$
log(x^2 + 6*x + 4)/2 - 3*log((2*x - 2*sqrt(5) + 6)/(2*x + 2*sqrt(5) + 6))/(2*sqrt(5))
Simplificación general
[src]
/ ___\
___ |3 + x - \/ 5 |
3*\/ 5 *log|-------------|
/ 2 \ | ___|
log\4 + x + 6*x/ \3 + x + \/ 5 /
----------------- - --------------------------
2 10
$$- \frac{3 \sqrt{5} \log{\left(\frac{x - \sqrt{5} + 3}{x + \sqrt{5} + 3} \right)}}{10} + \frac{\log{\left(x^{2} + 6 x + 4 \right)}}{2}$$
log(4 + x^2 + 6*x)/2 - 3*sqrt(5)*log((3 + x - sqrt(5))/(3 + x + sqrt(5)))/10
Parte trigonométrica
[src]
/ ___ \
___ |6 - 2*\/ 5 + 2*x|
3*\/ 5 *log|-----------------|
/ 2 \ | ___|
log\4 + x + 6*x/ \6 + 2*x + 2*\/ 5 /
----------------- - ------------------------------
2 10
$$- \frac{3 \sqrt{5} \log{\left(\frac{2 x - 2 \sqrt{5} + 6}{2 x + 2 \sqrt{5} + 6} \right)}}{10} + \frac{\log{\left(x^{2} + 6 x + 4 \right)}}{2}$$
log(4 + x^2 + 6*x)/2 - 3*sqrt(5)*log((6 - 2*sqrt(5) + 2*x)/(6 + 2*x + 2*sqrt(5)))/10
Respuesta numérica
[src]
0.5*log(x^2 + 6*x + 4) - 0.670820393249937*log((2*x - 2*sqrt(5) + 6)/(2*x + 2*sqrt(5) + 6))
0.5*log(x^2 + 6*x + 4) - 0.670820393249937*log((2*x - 2*sqrt(5) + 6)/(2*x + 2*sqrt(5) + 6))
Unión de expresiones racionales
[src]
/ ___\
___ |3 + x - \/ 5 |
5*log(4 + x*(6 + x)) - 3*\/ 5 *log|-------------|
| ___|
\3 + x + \/ 5 /
-------------------------------------------------
10
$$\frac{- 3 \sqrt{5} \log{\left(\frac{x - \sqrt{5} + 3}{x + \sqrt{5} + 3} \right)} + 5 \log{\left(x \left(x + 6\right) + 4 \right)}}{10}$$
(5*log(4 + x*(6 + x)) - 3*sqrt(5)*log((3 + x - sqrt(5))/(3 + x + sqrt(5))))/10
Potencias
[src]
/ ___ \
___ |6 - 2*\/ 5 + 2*x|
3*\/ 5 *log|-----------------|
/ 2 \ | ___|
log\4 + x + 6*x/ \6 + 2*x + 2*\/ 5 /
----------------- - ------------------------------
2 10
$$- \frac{3 \sqrt{5} \log{\left(\frac{2 x - 2 \sqrt{5} + 6}{2 x + 2 \sqrt{5} + 6} \right)}}{10} + \frac{\log{\left(x^{2} + 6 x + 4 \right)}}{2}$$
log(4 + x^2 + 6*x)/2 - 3*sqrt(5)*log((6 - 2*sqrt(5) + 2*x)/(6 + 2*x + 2*sqrt(5)))/10
Denominador común
[src]
/ ___ \
___ | 3 x \/ 5 |
3*\/ 5 *log|------------- + ------------- - -------------|
/ 2 \ | ___ ___ ___|
log\4 + x + 6*x/ \3 + x + \/ 5 3 + x + \/ 5 3 + x + \/ 5 /
----------------- - ----------------------------------------------------------
2 10
$$\frac{\log{\left(x^{2} + 6 x + 4 \right)}}{2} - \frac{3 \sqrt{5} \log{\left(\frac{x}{x + \sqrt{5} + 3} - \frac{\sqrt{5}}{x + \sqrt{5} + 3} + \frac{3}{x + \sqrt{5} + 3} \right)}}{10}$$
log(4 + x^2 + 6*x)/2 - 3*sqrt(5)*log(3/(3 + x + sqrt(5)) + x/(3 + x + sqrt(5)) - sqrt(5)/(3 + x + sqrt(5)))/10
Combinatoria
[src]
/ ___ \
___ | 6 2*\/ 5 2*x |
3*\/ 5 *log|----------------- - ----------------- + -----------------|
/ 2 \ | ___ ___ ___|
log\4 + x + 6*x/ \6 + 2*x + 2*\/ 5 6 + 2*x + 2*\/ 5 6 + 2*x + 2*\/ 5 /
----------------- - ----------------------------------------------------------------------
2 10
$$\frac{\log{\left(x^{2} + 6 x + 4 \right)}}{2} - \frac{3 \sqrt{5} \log{\left(\frac{2 x}{2 x + 2 \sqrt{5} + 6} - \frac{2 \sqrt{5}}{2 x + 2 \sqrt{5} + 6} + \frac{6}{2 x + 2 \sqrt{5} + 6} \right)}}{10}$$
log(4 + x^2 + 6*x)/2 - 3*sqrt(5)*log(6/(6 + 2*x + 2*sqrt(5)) - 2*sqrt(5)/(6 + 2*x + 2*sqrt(5)) + 2*x/(6 + 2*x + 2*sqrt(5)))/10
Compilar la expresión
[src]
/ ___ \
___ |2*x - 2*\/ 5 + 6|
3*\/ 5 *log|-----------------|
/ 2 \ | ___ |
log\x + 6*x + 4/ \2*x + 2*\/ 5 + 6/
----------------- - ------------------------------
2 10
$$- \frac{3 \sqrt{5} \log{\left(\frac{\left(2 x - 2 \sqrt{5}\right) + 6}{\left(2 x + 2 \sqrt{5}\right) + 6} \right)}}{10} + \frac{\log{\left(\left(x^{2} + 6 x\right) + 4 \right)}}{2}$$
log(x^2 + 6*x + 4)/2 - 3*sqrt(5)*log((2*x - 2*sqrt(5) + 6)/(2*x + 2*sqrt(5) + 6))/10
Denominador racional
[src]
/ ___ \
/ 2 \ ___ | 6 2*\/ 5 2*x |
5*log\4 + x + 6*x/ - 3*\/ 5 *log|----------------- - ----------------- + -----------------|
| ___ ___ ___ |
\2*x + 2*\/ 5 + 6 2*x + 2*\/ 5 + 6 2*x + 2*\/ 5 + 6/
--------------------------------------------------------------------------------------------
10
$$\frac{5 \log{\left(x^{2} + 6 x + 4 \right)} - 3 \sqrt{5} \log{\left(\frac{2 x}{\left(2 x + 2 \sqrt{5}\right) + 6} - \frac{2 \sqrt{5}}{\left(2 x + 2 \sqrt{5}\right) + 6} + \frac{6}{\left(2 x + 2 \sqrt{5}\right) + 6} \right)}}{10}$$
(5*log(4 + x^2 + 6*x) - 3*sqrt(5)*log(6/(2*x + 2*sqrt(5) + 6) - 2*sqrt(5)/(2*x + 2*sqrt(5) + 6) + 2*x/(2*x + 2*sqrt(5) + 6)))/10