Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(4*x^2+2*x-3)/8-(sqrt(13)*log((8*x-2*sqrt(13)+2)/(8*x+2*sqrt(13)+2)))/8
¿Cómo vas a descomponer esta log(4*x^2+2*x-3)/8-(sqrt(13)*log((8*x-2*sqrt(13)+2)/(8*x+2*sqrt(13)+2)))/8 expresión en fracciones?
Solución
Ha introducido
[src]
/ ____ \
____ |8*x - 2*\/ 13 + 2|
\/ 13 *log|------------------|
/ 2 \ | ____ |
log\4*x + 2*x - 3/ \8*x + 2*\/ 13 + 2/
------------------- - ------------------------------
8 8
$$- \frac{\sqrt{13} \log{\left(\frac{\left(8 x - 2 \sqrt{13}\right) + 2}{\left(8 x + 2 \sqrt{13}\right) + 2} \right)}}{8} + \frac{\log{\left(\left(4 x^{2} + 2 x\right) - 3 \right)}}{8}$$
log(4*x^2 + 2*x - 3)/8 - sqrt(13)*log((8*x - 2*sqrt(13) + 2)/(8*x + 2*sqrt(13) + 2))/8
Simplificación general
[src]
/ ____ \
____ |1 - \/ 13 + 4*x|
\/ 13 *log|----------------|
/ 2\ | ____ |
log\-3 + 2*x + 4*x / \1 + \/ 13 + 4*x/
-------------------- - ----------------------------
8 8
$$- \frac{\sqrt{13} \log{\left(\frac{4 x - \sqrt{13} + 1}{4 x + 1 + \sqrt{13}} \right)}}{8} + \frac{\log{\left(4 x^{2} + 2 x - 3 \right)}}{8}$$
log(-3 + 2*x + 4*x^2)/8 - sqrt(13)*log((1 - sqrt(13) + 4*x)/(1 + sqrt(13) + 4*x))/8
Respuesta numérica
[src]
0.125*log(4*x^2 + 2*x - 3) - 0.450693909432999*log((8*x - 2*sqrt(13) + 2)/(8*x + 2*sqrt(13) + 2))
0.125*log(4*x^2 + 2*x - 3) - 0.450693909432999*log((8*x - 2*sqrt(13) + 2)/(8*x + 2*sqrt(13) + 2))
Combinatoria
[src]
/ ____ \
____ | 2 2*\/ 13 8*x |
\/ 13 *log|------------------ - ------------------ + ------------------|
/ 2\ | ____ ____ ____ |
log\-3 + 2*x + 4*x / \2 + 2*\/ 13 + 8*x 2 + 2*\/ 13 + 8*x 2 + 2*\/ 13 + 8*x/
-------------------- - ------------------------------------------------------------------------
8 8
$$\frac{\log{\left(4 x^{2} + 2 x - 3 \right)}}{8} - \frac{\sqrt{13} \log{\left(\frac{8 x}{8 x + 2 + 2 \sqrt{13}} - \frac{2 \sqrt{13}}{8 x + 2 + 2 \sqrt{13}} + \frac{2}{8 x + 2 + 2 \sqrt{13}} \right)}}{8}$$
log(-3 + 2*x + 4*x^2)/8 - sqrt(13)*log(2/(2 + 2*sqrt(13) + 8*x) - 2*sqrt(13)/(2 + 2*sqrt(13) + 8*x) + 8*x/(2 + 2*sqrt(13) + 8*x))/8
Denominador común
[src]
/ ____ \
____ | 1 \/ 13 4*x |
\/ 13 *log|---------------- - ---------------- + ----------------|
/ 2\ | ____ ____ ____ |
log\-3 + 2*x + 4*x / \1 + \/ 13 + 4*x 1 + \/ 13 + 4*x 1 + \/ 13 + 4*x/
-------------------- - ------------------------------------------------------------------
8 8
$$\frac{\log{\left(4 x^{2} + 2 x - 3 \right)}}{8} - \frac{\sqrt{13} \log{\left(\frac{4 x}{4 x + 1 + \sqrt{13}} - \frac{\sqrt{13}}{4 x + 1 + \sqrt{13}} + \frac{1}{4 x + 1 + \sqrt{13}} \right)}}{8}$$
log(-3 + 2*x + 4*x^2)/8 - sqrt(13)*log(1/(1 + sqrt(13) + 4*x) - sqrt(13)/(1 + sqrt(13) + 4*x) + 4*x/(1 + sqrt(13) + 4*x))/8
Denominador racional
[src]
/ ____ \
____ | 2 2*\/ 13 8*x | / 2\
- \/ 13 *log|------------------ - ------------------ + ------------------| + log\-3 + 2*x + 4*x /
| ____ ____ ____ |
\8*x + 2*\/ 13 + 2 8*x + 2*\/ 13 + 2 8*x + 2*\/ 13 + 2/
-------------------------------------------------------------------------------------------------
8
$$\frac{\log{\left(4 x^{2} + 2 x - 3 \right)} - \sqrt{13} \log{\left(\frac{8 x}{\left(8 x + 2 \sqrt{13}\right) + 2} - \frac{2 \sqrt{13}}{\left(8 x + 2 \sqrt{13}\right) + 2} + \frac{2}{\left(8 x + 2 \sqrt{13}\right) + 2} \right)}}{8}$$
(-sqrt(13)*log(2/(8*x + 2*sqrt(13) + 2) - 2*sqrt(13)/(8*x + 2*sqrt(13) + 2) + 8*x/(8*x + 2*sqrt(13) + 2)) + log(-3 + 2*x + 4*x^2))/8
Potencias
[src]
/ ____ \
____ |2 - 2*\/ 13 + 8*x|
\/ 13 *log|------------------|
/ 2\ | ____ |
log\-3 + 2*x + 4*x / \2 + 2*\/ 13 + 8*x/
-------------------- - ------------------------------
8 8
$$- \frac{\sqrt{13} \log{\left(\frac{8 x - 2 \sqrt{13} + 2}{8 x + 2 + 2 \sqrt{13}} \right)}}{8} + \frac{\log{\left(4 x^{2} + 2 x - 3 \right)}}{8}$$
log(-3 + 2*x + 4*x^2)/8 - sqrt(13)*log((2 - 2*sqrt(13) + 8*x)/(2 + 2*sqrt(13) + 8*x))/8
Unión de expresiones racionales
[src]
/ ____ \
____ |1 - \/ 13 + 4*x|
- \/ 13 *log|----------------| + log(-3 + 2*x*(1 + 2*x))
| ____ |
\1 + \/ 13 + 4*x/
--------------------------------------------------------
8
$$\frac{- \sqrt{13} \log{\left(\frac{4 x - \sqrt{13} + 1}{4 x + 1 + \sqrt{13}} \right)} + \log{\left(2 x \left(2 x + 1\right) - 3 \right)}}{8}$$
(-sqrt(13)*log((1 - sqrt(13) + 4*x)/(1 + sqrt(13) + 4*x)) + log(-3 + 2*x*(1 + 2*x)))/8
Parte trigonométrica
[src]
/ ____ \
____ |2 - 2*\/ 13 + 8*x|
\/ 13 *log|------------------|
/ 2\ | ____ |
log\-3 + 2*x + 4*x / \2 + 2*\/ 13 + 8*x/
-------------------- - ------------------------------
8 8
$$- \frac{\sqrt{13} \log{\left(\frac{8 x - 2 \sqrt{13} + 2}{8 x + 2 + 2 \sqrt{13}} \right)}}{8} + \frac{\log{\left(4 x^{2} + 2 x - 3 \right)}}{8}$$
log(-3 + 2*x + 4*x^2)/8 - sqrt(13)*log((2 - 2*sqrt(13) + 8*x)/(2 + 2*sqrt(13) + 8*x))/8