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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x^2+5*x+3)/2-(5*log((2*x-sqrt(13)+5)/(5+sqrt(13)+2*x)))/(2*sqrt(13))

¿Cómo vas a descomponer esta log(x^2+5*x+3)/2-(5*log((2*x-sqrt(13)+5)/(5+sqrt(13)+2*x)))/(2*sqrt(13)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                         /        ____    \
                         |2*x - \/ 13  + 5|
                    5*log|----------------|
   / 2          \        |      ____      |
log\x  + 5*x + 3/        \5 + \/ 13  + 2*x/
----------------- - -----------------------
        2                       ____       
                            2*\/ 13
−5log⁡((2x−13)+52x+(13+5))213+log⁡((x2+5x)+3)2- \frac{5 \log{\left(\frac{\left(2 x - \sqrt{13}\right) + 5}{2 x + \left(\sqrt{13} + 5\right)} \right)}}{2 \sqrt{13}} + \frac{\log{\left(\left(x^{2} + 5 x\right) + 3 \right)}}{2} 
log(x^2 + 5*x + 3)/2 - 5*log((2*x - sqrt(13) + 5)/(5 + sqrt(13) + 2*x))/(2*sqrt(13))
Simplificación general [src] 
                                /      ____      \
                        ____    |5 - \/ 13  + 2*x|
                    5*\/ 13 *log|----------------|
   /     2      \               |      ____      |
log\3 + x  + 5*x/               \5 + \/ 13  + 2*x/
----------------- - ------------------------------
        2                         26
−513log⁡(2x−13+52x+13+5)26+log⁡(x2+5x+3)2- \frac{5 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 5}{2 x + \sqrt{13} + 5} \right)}}{26} + \frac{\log{\left(x^{2} + 5 x + 3 \right)}}{2} 
log(3 + x^2 + 5*x)/2 - 5*sqrt(13)*log((5 - sqrt(13) + 2*x)/(5 + sqrt(13) + 2*x))/26
Combinatoria [src] 
                                /                          ____                        \
                        ____    |       5                \/ 13               2*x       |
                    5*\/ 13 *log|---------------- - ---------------- + ----------------|
   /     2      \               |      ____               ____               ____      |
log\3 + x  + 5*x/               \5 + \/ 13  + 2*x   5 + \/ 13  + 2*x   5 + \/ 13  + 2*x/
----------------- - --------------------------------------------------------------------
        2                                            26
log⁡(x2+5x+3)2−513log⁡(2x2x+13+5−132x+13+5+52x+13+5)26\frac{\log{\left(x^{2} + 5 x + 3 \right)}}{2} - \frac{5 \sqrt{13} \log{\left(\frac{2 x}{2 x + \sqrt{13} + 5} - \frac{\sqrt{13}}{2 x + \sqrt{13} + 5} + \frac{5}{2 x + \sqrt{13} + 5} \right)}}{26} 
log(3 + x^2 + 5*x)/2 - 5*sqrt(13)*log(5/(5 + sqrt(13) + 2*x) - sqrt(13)/(5 + sqrt(13) + 2*x) + 2*x/(5 + sqrt(13) + 2*x))/26
Denominador racional [src] 
                                   /                          ____                        \
      /     2      \       ____    |       5                \/ 13               2*x       |
13*log\3 + x  + 5*x/ - 5*\/ 13 *log|---------------- - ---------------- + ----------------|
                                   |      ____               ____               ____      |
                                   \5 + \/ 13  + 2*x   5 + \/ 13  + 2*x   5 + \/ 13  + 2*x/
-------------------------------------------------------------------------------------------
                                             26
13log⁡(x2+5x+3)−513log⁡(2x2x+(13+5)−132x+(13+5)+52x+(13+5))26\frac{13 \log{\left(x^{2} + 5 x + 3 \right)} - 5 \sqrt{13} \log{\left(\frac{2 x}{2 x + \left(\sqrt{13} + 5\right)} - \frac{\sqrt{13}}{2 x + \left(\sqrt{13} + 5\right)} + \frac{5}{2 x + \left(\sqrt{13} + 5\right)} \right)}}{26} 
(13*log(3 + x^2 + 5*x) - 5*sqrt(13)*log(5/(5 + sqrt(13) + 2*x) - sqrt(13)/(5 + sqrt(13) + 2*x) + 2*x/(5 + sqrt(13) + 2*x)))/26
Respuesta numérica [src] 
0.5*log(x^2 + 5*x + 3) - 0.693375245281536*log((2*x - sqrt(13) + 5)/(5 + sqrt(13) + 2*x))
0.5*log(x^2 + 5*x + 3) - 0.693375245281536*log((2*x - sqrt(13) + 5)/(5 + sqrt(13) + 2*x))
Denominador común [src] 
                                /                          ____                        \
                        ____    |       5                \/ 13               2*x       |
                    5*\/ 13 *log|---------------- - ---------------- + ----------------|
   /     2      \               |      ____               ____               ____      |
log\3 + x  + 5*x/               \5 + \/ 13  + 2*x   5 + \/ 13  + 2*x   5 + \/ 13  + 2*x/
----------------- - --------------------------------------------------------------------
        2                                            26
log⁡(x2+5x+3)2−513log⁡(2x2x+13+5−132x+13+5+52x+13+5)26\frac{\log{\left(x^{2} + 5 x + 3 \right)}}{2} - \frac{5 \sqrt{13} \log{\left(\frac{2 x}{2 x + \sqrt{13} + 5} - \frac{\sqrt{13}}{2 x + \sqrt{13} + 5} + \frac{5}{2 x + \sqrt{13} + 5} \right)}}{26} 
log(3 + x^2 + 5*x)/2 - 5*sqrt(13)*log(5/(5 + sqrt(13) + 2*x) - sqrt(13)/(5 + sqrt(13) + 2*x) + 2*x/(5 + sqrt(13) + 2*x))/26
Unión de expresiones racionales [src] 
                                    /      ____      \
                            ____    |5 - \/ 13  + 2*x|
13*log(3 + x*(5 + x)) - 5*\/ 13 *log|----------------|
                                    |      ____      |
                                    \5 + \/ 13  + 2*x/
------------------------------------------------------
                          26
−513log⁡(2x−13+52x+13+5)+13log⁡(x(x+5)+3)26\frac{- 5 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 5}{2 x + \sqrt{13} + 5} \right)} + 13 \log{\left(x \left(x + 5\right) + 3 \right)}}{26} 
(13*log(3 + x*(5 + x)) - 5*sqrt(13)*log((5 - sqrt(13) + 2*x)/(5 + sqrt(13) + 2*x)))/26
Potencias [src] 
                                /      ____      \
                        ____    |5 - \/ 13  + 2*x|
                    5*\/ 13 *log|----------------|
   /     2      \               |      ____      |
log\3 + x  + 5*x/               \5 + \/ 13  + 2*x/
----------------- - ------------------------------
        2                         26
−513log⁡(2x−13+52x+13+5)26+log⁡(x2+5x+3)2- \frac{5 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 5}{2 x + \sqrt{13} + 5} \right)}}{26} + \frac{\log{\left(x^{2} + 5 x + 3 \right)}}{2} 
log(3 + x^2 + 5*x)/2 - 5*sqrt(13)*log((5 - sqrt(13) + 2*x)/(5 + sqrt(13) + 2*x))/26
Parte trigonométrica [src] 
                                /      ____      \
                        ____    |5 - \/ 13  + 2*x|
                    5*\/ 13 *log|----------------|
   /     2      \               |      ____      |
log\3 + x  + 5*x/               \5 + \/ 13  + 2*x/
----------------- - ------------------------------
        2                         26
−513log⁡(2x−13+52x+13+5)26+log⁡(x2+5x+3)2- \frac{5 \sqrt{13} \log{\left(\frac{2 x - \sqrt{13} + 5}{2 x + \sqrt{13} + 5} \right)}}{26} + \frac{\log{\left(x^{2} + 5 x + 3 \right)}}{2} 
log(3 + x^2 + 5*x)/2 - 5*sqrt(13)*log((5 - sqrt(13) + 2*x)/(5 + sqrt(13) + 2*x))/26
Compilar la expresión [src] 
                                /        ____    \
                        ____    |2*x - \/ 13  + 5|
                    5*\/ 13 *log|----------------|
   / 2          \               |      ____      |
log\x  + 5*x + 3/               \5 + \/ 13  + 2*x/
----------------- - ------------------------------
        2                         26
−513log⁡((2x−13)+52x+(13+5))26+log⁡((x2+5x)+3)2- \frac{5 \sqrt{13} \log{\left(\frac{\left(2 x - \sqrt{13}\right) + 5}{2 x + \left(\sqrt{13} + 5\right)} \right)}}{26} + \frac{\log{\left(\left(x^{2} + 5 x\right) + 3 \right)}}{2} 
log(x^2 + 5*x + 3)/2 - 5*sqrt(13)*log((2*x - sqrt(13) + 5)/(5 + sqrt(13) + 2*x))/26
Abrimos la expresión [src] 
                                /        ____    \
                        ____    |2*x - \/ 13  + 5|
                    5*\/ 13 *log|----------------|
   / 2          \               |      ____      |
log\x  + 5*x + 3/               \5 + \/ 13  + 2*x/
----------------- - ------------------------------
        2                         26
−513log⁡((2x−13)+52x+(13+5))26+log⁡((x2+5x)+3)2- \frac{5 \sqrt{13} \log{\left(\frac{\left(2 x - \sqrt{13}\right) + 5}{2 x + \left(\sqrt{13} + 5\right)} \right)}}{26} + \frac{\log{\left(\left(x^{2} + 5 x\right) + 3 \right)}}{2} 
log(x^2 + 5*x + 3)/2 - 5*sqrt(13)*log((2*x - sqrt(13) + 5)/(5 + sqrt(13) + 2*x))/26
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