Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(x^2+5*x-2)/2-(5*log((2*x-sqrt(33)+5)/(2*x+sqrt(33)+5)))/(2*sqrt(33))
¿Cómo vas a descomponer esta log(x^2+5*x-2)/2-(5*log((2*x-sqrt(33)+5)/(2*x+sqrt(33)+5)))/(2*sqrt(33)) expresión en fracciones?
Solución
Ha introducido
[src]
/ ____ \
|2*x - \/ 33 + 5|
5*log|----------------|
/ 2 \ | ____ |
log\x + 5*x - 2/ \2*x + \/ 33 + 5/
----------------- - -----------------------
2 ____
2*\/ 33
$$- \frac{5 \log{\left(\frac{\left(2 x - \sqrt{33}\right) + 5}{\left(2 x + \sqrt{33}\right) + 5} \right)}}{2 \sqrt{33}} + \frac{\log{\left(\left(x^{2} + 5 x\right) - 2 \right)}}{2}$$
log(x^2 + 5*x - 2)/2 - 5*log((2*x - sqrt(33) + 5)/(2*x + sqrt(33) + 5))/(2*sqrt(33))
Simplificación general
[src]
/ ____ \
____ |5 - \/ 33 + 2*x|
5*\/ 33 *log|----------------|
/ 2 \ | ____ |
log\-2 + x + 5*x/ \5 + \/ 33 + 2*x/
------------------ - ------------------------------
2 66
$$- \frac{5 \sqrt{33} \log{\left(\frac{2 x - \sqrt{33} + 5}{2 x + 5 + \sqrt{33}} \right)}}{66} + \frac{\log{\left(x^{2} + 5 x - 2 \right)}}{2}$$
log(-2 + x^2 + 5*x)/2 - 5*sqrt(33)*log((5 - sqrt(33) + 2*x)/(5 + sqrt(33) + 2*x))/66
Potencias
[src]
/ ____ \
____ |5 - \/ 33 + 2*x|
5*\/ 33 *log|----------------|
/ 2 \ | ____ |
log\-2 + x + 5*x/ \5 + \/ 33 + 2*x/
------------------ - ------------------------------
2 66
$$- \frac{5 \sqrt{33} \log{\left(\frac{2 x - \sqrt{33} + 5}{2 x + 5 + \sqrt{33}} \right)}}{66} + \frac{\log{\left(x^{2} + 5 x - 2 \right)}}{2}$$
log(-2 + x^2 + 5*x)/2 - 5*sqrt(33)*log((5 - sqrt(33) + 2*x)/(5 + sqrt(33) + 2*x))/66
Parte trigonométrica
[src]
/ ____ \
____ |5 - \/ 33 + 2*x|
5*\/ 33 *log|----------------|
/ 2 \ | ____ |
log\-2 + x + 5*x/ \5 + \/ 33 + 2*x/
------------------ - ------------------------------
2 66
$$- \frac{5 \sqrt{33} \log{\left(\frac{2 x - \sqrt{33} + 5}{2 x + 5 + \sqrt{33}} \right)}}{66} + \frac{\log{\left(x^{2} + 5 x - 2 \right)}}{2}$$
log(-2 + x^2 + 5*x)/2 - 5*sqrt(33)*log((5 - sqrt(33) + 2*x)/(5 + sqrt(33) + 2*x))/66
Denominador racional
[src]
/ ____ \
/ 2 \ ____ | 5 \/ 33 2*x |
33*log\-2 + x + 5*x/ - 5*\/ 33 *log|---------------- - ---------------- + ----------------|
| ____ ____ ____ |
\2*x + \/ 33 + 5 2*x + \/ 33 + 5 2*x + \/ 33 + 5/
--------------------------------------------------------------------------------------------
66
$$\frac{33 \log{\left(x^{2} + 5 x - 2 \right)} - 5 \sqrt{33} \log{\left(\frac{2 x}{\left(2 x + \sqrt{33}\right) + 5} - \frac{\sqrt{33}}{\left(2 x + \sqrt{33}\right) + 5} + \frac{5}{\left(2 x + \sqrt{33}\right) + 5} \right)}}{66}$$
(33*log(-2 + x^2 + 5*x) - 5*sqrt(33)*log(5/(2*x + sqrt(33) + 5) - sqrt(33)/(2*x + sqrt(33) + 5) + 2*x/(2*x + sqrt(33) + 5)))/66
Denominador común
[src]
/ ____ \
____ | 5 \/ 33 2*x |
5*\/ 33 *log|---------------- - ---------------- + ----------------|
/ 2 \ | ____ ____ ____ |
log\-2 + x + 5*x/ \5 + \/ 33 + 2*x 5 + \/ 33 + 2*x 5 + \/ 33 + 2*x/
------------------ - --------------------------------------------------------------------
2 66
$$\frac{\log{\left(x^{2} + 5 x - 2 \right)}}{2} - \frac{5 \sqrt{33} \log{\left(\frac{2 x}{2 x + 5 + \sqrt{33}} - \frac{\sqrt{33}}{2 x + 5 + \sqrt{33}} + \frac{5}{2 x + 5 + \sqrt{33}} \right)}}{66}$$
log(-2 + x^2 + 5*x)/2 - 5*sqrt(33)*log(5/(5 + sqrt(33) + 2*x) - sqrt(33)/(5 + sqrt(33) + 2*x) + 2*x/(5 + sqrt(33) + 2*x))/66
Compilar la expresión
[src]
/ ____ \
____ |2*x - \/ 33 + 5|
5*\/ 33 *log|----------------|
/ 2 \ | ____ |
log\x + 5*x - 2/ \2*x + \/ 33 + 5/
----------------- - ------------------------------
2 66
$$- \frac{5 \sqrt{33} \log{\left(\frac{\left(2 x - \sqrt{33}\right) + 5}{\left(2 x + \sqrt{33}\right) + 5} \right)}}{66} + \frac{\log{\left(\left(x^{2} + 5 x\right) - 2 \right)}}{2}$$
log(x^2 + 5*x - 2)/2 - 5*sqrt(33)*log((2*x - sqrt(33) + 5)/(2*x + sqrt(33) + 5))/66
Respuesta numérica
[src]
0.5*log(x^2 + 5*x - 2) - 0.435194139889245*log((2*x - sqrt(33) + 5)/(2*x + sqrt(33) + 5))
0.5*log(x^2 + 5*x - 2) - 0.435194139889245*log((2*x - sqrt(33) + 5)/(2*x + sqrt(33) + 5))
Unión de expresiones racionales
[src]
/ ____ \
____ |5 - \/ 33 + 2*x|
33*log(-2 + x*(5 + x)) - 5*\/ 33 *log|----------------|
| ____ |
\5 + \/ 33 + 2*x/
-------------------------------------------------------
66
$$\frac{- 5 \sqrt{33} \log{\left(\frac{2 x - \sqrt{33} + 5}{2 x + 5 + \sqrt{33}} \right)} + 33 \log{\left(x \left(x + 5\right) - 2 \right)}}{66}$$
(33*log(-2 + x*(5 + x)) - 5*sqrt(33)*log((5 - sqrt(33) + 2*x)/(5 + sqrt(33) + 2*x)))/66
Combinatoria
[src]
/ ____ \
____ | 5 \/ 33 2*x |
5*\/ 33 *log|---------------- - ---------------- + ----------------|
/ 2 \ | ____ ____ ____ |
log\-2 + x + 5*x/ \5 + \/ 33 + 2*x 5 + \/ 33 + 2*x 5 + \/ 33 + 2*x/
------------------ - --------------------------------------------------------------------
2 66
$$\frac{\log{\left(x^{2} + 5 x - 2 \right)}}{2} - \frac{5 \sqrt{33} \log{\left(\frac{2 x}{2 x + 5 + \sqrt{33}} - \frac{\sqrt{33}}{2 x + 5 + \sqrt{33}} + \frac{5}{2 x + 5 + \sqrt{33}} \right)}}{66}$$
log(-2 + x^2 + 5*x)/2 - 5*sqrt(33)*log(5/(5 + sqrt(33) + 2*x) - sqrt(33)/(5 + sqrt(33) + 2*x) + 2*x/(5 + sqrt(33) + 2*x))/66