Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log((2*sqrt(x^3+3)-2*sqrt(3))/(2*sqrt(3)+2*sqrt(x^3+3)))/3^(3/2)
¿Cómo vas a descomponer esta log((2*sqrt(x^3+3)-2*sqrt(3))/(2*sqrt(3)+2*sqrt(x^3+3)))/3^(3/2) expresión en fracciones?
Solución
Ha introducido
[src]
/ ________ \
| / 3 ___|
|2*\/ x + 3 - 2*\/ 3 |
log|-----------------------|
| ________|
| ___ / 3 |
\2*\/ 3 + 2*\/ x + 3 /
----------------------------
3/2
3
$$\frac{\log{\left(\frac{2 \sqrt{x^{3} + 3} - 2 \sqrt{3}}{2 \sqrt{x^{3} + 3} + 2 \sqrt{3}} \right)}}{3^{\frac{3}{2}}}$$
log((2*sqrt(x^3 + 3) - 2*sqrt(3))/(2*sqrt(3) + 2*sqrt(x^3 + 3)))/3^(3/2)
Simplificación general
[src]
/ ________ \
| / 3 ___|
___ |\/ 3 + x - \/ 3 |
\/ 3 *log|-------------------|
| ________|
| ___ / 3 |
\\/ 3 + \/ 3 + x /
------------------------------
9
$$\frac{\sqrt{3} \log{\left(\frac{\sqrt{x^{3} + 3} - \sqrt{3}}{\sqrt{x^{3} + 3} + \sqrt{3}} \right)}}{9}$$
sqrt(3)*log((sqrt(3 + x^3) - sqrt(3))/(sqrt(3) + sqrt(3 + x^3)))/9
Descomposición de una fracción
[src]
sqrt(3)*log(-2*sqrt(3)/(2*sqrt(3) + 2*sqrt(x^3 + 3)) + 2*sqrt(x^3 + 3)/(2*sqrt(3) + 2*sqrt(x^3 + 3)))/9
$$\frac{\sqrt{3} \log{\left(\frac{2 \sqrt{x^{3} + 3}}{2 \sqrt{x^{3} + 3} + 2 \sqrt{3}} - \frac{2 \sqrt{3}}{2 \sqrt{x^{3} + 3} + 2 \sqrt{3}} \right)}}{9}$$
/ ________ \
| ___ / 3 |
___ | 2*\/ 3 2*\/ x + 3 |
\/ 3 *log|- ----------------------- + -----------------------|
| ________ ________|
| ___ / 3 ___ / 3 |
\ 2*\/ 3 + 2*\/ x + 3 2*\/ 3 + 2*\/ x + 3 /
--------------------------------------------------------------
9
Respuesta numérica
[src]
0.192450089729875*log((2*sqrt(x^3 + 3) - 2*sqrt(3))/(2*sqrt(3) + 2*sqrt(x^3 + 3)))
0.192450089729875*log((2*sqrt(x^3 + 3) - 2*sqrt(3))/(2*sqrt(3) + 2*sqrt(x^3 + 3)))
Parte trigonométrica
[src]
/ ________\
| ___ / 3 |
___ |- 2*\/ 3 + 2*\/ 3 + x |
\/ 3 *log|-------------------------|
| ________ |
| ___ / 3 |
\ 2*\/ 3 + 2*\/ 3 + x /
------------------------------------
9
$$\frac{\sqrt{3} \log{\left(\frac{2 \sqrt{x^{3} + 3} - 2 \sqrt{3}}{2 \sqrt{x^{3} + 3} + 2 \sqrt{3}} \right)}}{9}$$
sqrt(3)*log((-2*sqrt(3) + 2*sqrt(3 + x^3))/(2*sqrt(3) + 2*sqrt(3 + x^3)))/9
Combinatoria
[src]
/ ________ \
| ___ / 3 |
___ | 2*\/ 3 2*\/ 3 + x |
\/ 3 *log|- ----------------------- + -----------------------|
| ________ ________|
| ___ / 3 ___ / 3 |
\ 2*\/ 3 + 2*\/ 3 + x 2*\/ 3 + 2*\/ 3 + x /
--------------------------------------------------------------
9
$$\frac{\sqrt{3} \log{\left(\frac{2 \sqrt{x^{3} + 3}}{2 \sqrt{x^{3} + 3} + 2 \sqrt{3}} - \frac{2 \sqrt{3}}{2 \sqrt{x^{3} + 3} + 2 \sqrt{3}} \right)}}{9}$$
sqrt(3)*log(-2*sqrt(3)/(2*sqrt(3) + 2*sqrt(3 + x^3)) + 2*sqrt(3 + x^3)/(2*sqrt(3) + 2*sqrt(3 + x^3)))/9
Potencias
[src]
/ ________\
| ___ / 3 |
___ |- 2*\/ 3 + 2*\/ 3 + x |
\/ 3 *log|-------------------------|
| ________ |
| ___ / 3 |
\ 2*\/ 3 + 2*\/ 3 + x /
------------------------------------
9
$$\frac{\sqrt{3} \log{\left(\frac{2 \sqrt{x^{3} + 3} - 2 \sqrt{3}}{2 \sqrt{x^{3} + 3} + 2 \sqrt{3}} \right)}}{9}$$
sqrt(3)*log((-2*sqrt(3) + 2*sqrt(3 + x^3))/(2*sqrt(3) + 2*sqrt(3 + x^3)))/9
Unión de expresiones racionales
[src]
/ ________ \
| / 3 ___|
___ |\/ 3 + x - \/ 3 |
\/ 3 *log|-------------------|
| ________|
| ___ / 3 |
\\/ 3 + \/ 3 + x /
------------------------------
9
$$\frac{\sqrt{3} \log{\left(\frac{\sqrt{x^{3} + 3} - \sqrt{3}}{\sqrt{x^{3} + 3} + \sqrt{3}} \right)}}{9}$$
sqrt(3)*log((sqrt(3 + x^3) - sqrt(3))/(sqrt(3) + sqrt(3 + x^3)))/9
Denominador común
[src]
/ ________ \
| / 3 ___ |
___ | \/ 3 + x \/ 3 |
\/ 3 *log|------------------- - -------------------|
| ________ ________|
| ___ / 3 ___ / 3 |
\\/ 3 + \/ 3 + x \/ 3 + \/ 3 + x /
----------------------------------------------------
9
$$\frac{\sqrt{3} \log{\left(\frac{\sqrt{x^{3} + 3}}{\sqrt{x^{3} + 3} + \sqrt{3}} - \frac{\sqrt{3}}{\sqrt{x^{3} + 3} + \sqrt{3}} \right)}}{9}$$
sqrt(3)*log(sqrt(3 + x^3)/(sqrt(3) + sqrt(3 + x^3)) - sqrt(3)/(sqrt(3) + sqrt(3 + x^3)))/9
Denominador racional
[src]
/ ________ ________ ________ ________\
| / 3 / 3 ___ / 3 ___ / 3 |
___ |3 + \/ 3 + x *\/ x + 3 - \/ 3 *\/ 3 + x - \/ 3 *\/ x + 3 |
\/ 3 *log|-------------------------------------------------------------------|
| 3 |
\ x /
------------------------------------------------------------------------------
9
$$\frac{\sqrt{3} \log{\left(\frac{\sqrt{x^{3} + 3} \sqrt{x^{3} + 3} - \sqrt{3} \sqrt{x^{3} + 3} - \sqrt{3} \sqrt{x^{3} + 3} + 3}{x^{3}} \right)}}{9}$$
sqrt(3)*log((3 + sqrt(3 + x^3)*sqrt(x^3 + 3) - sqrt(3)*sqrt(3 + x^3) - sqrt(3)*sqrt(x^3 + 3))/x^3)/9
Compilar la expresión
[src]
/ ________ \
| / 3 ___|
___ |2*\/ x + 3 - 2*\/ 3 |
\/ 3 *log|-----------------------|
| ________|
| ___ / 3 |
\2*\/ 3 + 2*\/ x + 3 /
----------------------------------
9
$$\frac{\sqrt{3} \log{\left(\frac{2 \sqrt{x^{3} + 3} - 2 \sqrt{3}}{2 \sqrt{x^{3} + 3} + 2 \sqrt{3}} \right)}}{9}$$
sqrt(3)*log((2*sqrt(x^3 + 3) - 2*sqrt(3))/(2*sqrt(3) + 2*sqrt(x^3 + 3)))/9