Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log((10*x-2*sqrt(5))/(2*sqrt(5)+10*x))/(2*sqrt(5))-log(5*x^2-1)/5
¿Cómo vas a descomponer esta log((10*x-2*sqrt(5))/(2*sqrt(5)+10*x))/(2*sqrt(5))-log(5*x^2-1)/5 expresión en fracciones?
Solución
Ha introducido
[src]
/ ___\
|10*x - 2*\/ 5 |
log|--------------|
| ___ | / 2 \
\2*\/ 5 + 10*x/ log\5*x - 1/
------------------- - -------------
___ 5
2*\/ 5
$$\frac{\log{\left(\frac{10 x - 2 \sqrt{5}}{10 x + 2 \sqrt{5}} \right)}}{2 \sqrt{5}} - \frac{\log{\left(5 x^{2} - 1 \right)}}{5}$$
log((10*x - 2*sqrt(5))/(2*sqrt(5) + 10*x))/((2*sqrt(5))) - log(5*x^2 - 1)/5
Simplificación general
[src]
/ ___ \
___ |- \/ 5 + 5*x|
\/ 5 *log|-------------|
/ 2\ | ___ |
log\-1 + 5*x / \ \/ 5 + 5*x /
- -------------- + ------------------------
5 10
$$\frac{\sqrt{5} \log{\left(\frac{5 x - \sqrt{5}}{5 x + \sqrt{5}} \right)}}{10} - \frac{\log{\left(5 x^{2} - 1 \right)}}{5}$$
-log(-1 + 5*x^2)/5 + sqrt(5)*log((-sqrt(5) + 5*x)/(sqrt(5) + 5*x))/10
Respuesta numérica
[src]
0.223606797749979*log((10*x - 2*sqrt(5))/(2*sqrt(5) + 10*x)) - 0.2*log(5*x^2 - 1)
0.223606797749979*log((10*x - 2*sqrt(5))/(2*sqrt(5) + 10*x)) - 0.2*log(5*x^2 - 1)
Unión de expresiones racionales
[src]
/ ___ \
/ 2\ ___ |- \/ 5 + 5*x|
- 2*log\-1 + 5*x / + \/ 5 *log|-------------|
| ___ |
\ \/ 5 + 5*x /
---------------------------------------------
10
$$\frac{\sqrt{5} \log{\left(\frac{5 x - \sqrt{5}}{5 x + \sqrt{5}} \right)} - 2 \log{\left(5 x^{2} - 1 \right)}}{10}$$
(-2*log(-1 + 5*x^2) + sqrt(5)*log((-sqrt(5) + 5*x)/(sqrt(5) + 5*x)))/10
Parte trigonométrica
[src]
/ ___ \
___ |- 2*\/ 5 + 10*x|
\/ 5 *log|----------------|
/ 2\ | ___ |
log\-1 + 5*x / \ 2*\/ 5 + 10*x /
- -------------- + ---------------------------
5 10
$$\frac{\sqrt{5} \log{\left(\frac{10 x - 2 \sqrt{5}}{10 x + 2 \sqrt{5}} \right)}}{10} - \frac{\log{\left(5 x^{2} - 1 \right)}}{5}$$
-log(-1 + 5*x^2)/5 + sqrt(5)*log((-2*sqrt(5) + 10*x)/(2*sqrt(5) + 10*x))/10
Combinatoria
[src]
/ ___ \
___ | 2*\/ 5 10*x |
\/ 5 *log|- -------------- + --------------|
/ 2\ | ___ ___ |
log\-1 + 5*x / \ 2*\/ 5 + 10*x 2*\/ 5 + 10*x/
- -------------- + --------------------------------------------
5 10
$$- \frac{\log{\left(5 x^{2} - 1 \right)}}{5} + \frac{\sqrt{5} \log{\left(\frac{10 x}{10 x + 2 \sqrt{5}} - \frac{2 \sqrt{5}}{10 x + 2 \sqrt{5}} \right)}}{10}$$
-log(-1 + 5*x^2)/5 + sqrt(5)*log(-2*sqrt(5)/(2*sqrt(5) + 10*x) + 10*x/(2*sqrt(5) + 10*x))/10
Denominador racional
[src]
/ 2 ___ \
/ 2\ ___ | 20 100*x 40*x*\/ 5 |
- 2*log\-1 + 5*x / + \/ 5 *log|------------ + ------------ - ------------|
| 2 2 2|
\-20 + 100*x -20 + 100*x -20 + 100*x /
--------------------------------------------------------------------------
10
$$\frac{- 2 \log{\left(5 x^{2} - 1 \right)} + \sqrt{5} \log{\left(\frac{100 x^{2}}{100 x^{2} - 20} - \frac{40 \sqrt{5} x}{100 x^{2} - 20} + \frac{20}{100 x^{2} - 20} \right)}}{10}$$
(-2*log(-1 + 5*x^2) + sqrt(5)*log(20/(-20 + 100*x^2) + 100*x^2/(-20 + 100*x^2) - 40*x*sqrt(5)/(-20 + 100*x^2)))/10
Denominador común
[src]
/ ___ \
___ | \/ 5 5*x |
\/ 5 *log|- ----------- + -----------|
/ 2\ | ___ ___ |
log\-1 + 5*x / \ \/ 5 + 5*x \/ 5 + 5*x/
- -------------- + --------------------------------------
5 10
$$- \frac{\log{\left(5 x^{2} - 1 \right)}}{5} + \frac{\sqrt{5} \log{\left(\frac{5 x}{5 x + \sqrt{5}} - \frac{\sqrt{5}}{5 x + \sqrt{5}} \right)}}{10}$$
-log(-1 + 5*x^2)/5 + sqrt(5)*log(-sqrt(5)/(sqrt(5) + 5*x) + 5*x/(sqrt(5) + 5*x))/10
Compilar la expresión
[src]
/ ___\
___ |10*x - 2*\/ 5 |
\/ 5 *log|--------------|
/ 2 \ | ___ |
log\5*x - 1/ \2*\/ 5 + 10*x/
- ------------- + -------------------------
5 10
$$\frac{\sqrt{5} \log{\left(\frac{10 x - 2 \sqrt{5}}{10 x + 2 \sqrt{5}} \right)}}{10} - \frac{\log{\left(5 x^{2} - 1 \right)}}{5}$$
-log(5*x^2 - 1)/5 + sqrt(5)*log((10*x - 2*sqrt(5))/(2*sqrt(5) + 10*x))/10
Potencias
[src]
/ ___ \
___ |- 2*\/ 5 + 10*x|
\/ 5 *log|----------------|
/ 2\ | ___ |
log\-1 + 5*x / \ 2*\/ 5 + 10*x /
- -------------- + ---------------------------
5 10
$$\frac{\sqrt{5} \log{\left(\frac{10 x - 2 \sqrt{5}}{10 x + 2 \sqrt{5}} \right)}}{10} - \frac{\log{\left(5 x^{2} - 1 \right)}}{5}$$
-log(-1 + 5*x^2)/5 + sqrt(5)*log((-2*sqrt(5) + 10*x)/(2*sqrt(5) + 10*x))/10