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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x+e)^acos(x)*(-log(log(x+e))/sqrt(1-x^2)+acos(x)/((x+e)*log(x+e)))

¿Cómo vas a descomponer esta log(x+e)^acos(x)*(-log(log(x+e))/sqrt(1-x^2)+acos(x)/((x+e)*log(x+e))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   acos(x)        /-log(log(x + E))         acos(x)      \
log       (x + E)*|----------------- + ------------------|
                  |      ________      (x + E)*log(x + E)|
                  |     /      2                         |
                  \   \/  1 - x                          /
((−1)log⁡(log⁡(x+e))1−x2+acos⁡(x)(x+e)log⁡(x+e))log⁡(x+e)acos⁡(x)\left(\frac{\left(-1\right) \log{\left(\log{\left(x + e \right)} \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{\left(x + e\right) \log{\left(x + e \right)}}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} 
log(x + E)^acos(x)*((-log(log(x + E)))/sqrt(1 - x^2) + acos(x)/(((x + E)*log(x + E))))
Simplificación general [src] 
                       /   ________                                             \
   -1 + acos(x)        |  /      2                                              |
log            (E + x)*\\/  1 - x  *acos(x) - (E + x)*log(E + x)*log(log(E + x))/
---------------------------------------------------------------------------------
                                  ________                                       
                                 /      2                                        
                               \/  1 - x  *(E + x)
(1−x2acos⁡(x)−(x+e)log⁡(x+e)log⁡(log⁡(x+e)))log⁡(x+e)acos⁡(x)−11−x2(x+e)\frac{\left(\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} - \left(x + e\right) \log{\left(x + e \right)} \log{\left(\log{\left(x + e \right)} \right)}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)} - 1}}{\sqrt{1 - x^{2}} \left(x + e\right)} 
log(E + x)^(-1 + acos(x))*(sqrt(1 - x^2)*acos(x) - (E + x)*log(E + x)*log(log(E + x)))/(sqrt(1 - x^2)*(E + x))
Respuesta numérica [src] 
log(x + E)^acos(x)*(-(1.0 - x^2)^(-0.5)*log(log(x + E)) + acos(x)/((2.71828182845905 + x)*log(x + E)))
log(x + E)^acos(x)*(-(1.0 - x^2)^(-0.5)*log(log(x + E)) + acos(x)/((2.71828182845905 + x)*log(x + E)))
Denominador racional [src] 
                                                                            ________                                                          ________                                                  
     -1 + acos(x)                   2    -1 + acos(x)                      /      2     -1 + acos(x)                                         /      2     -1 + acos(x)                                  
- log            (E + x)*acos(x) + x *log            (E + x)*acos(x) + E*\/  1 - x  *log            (E + x)*log(E + x)*log(log(E + x)) + x*\/  1 - x  *log            (E + x)*log(E + x)*log(log(E + x))
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                           /      2\                                                                                                    
                                                                                           \-1 + x /*(E + x)
x2log⁡(x+e)acos⁡(x)−1acos⁡(x)+x1−x2log⁡(x+e)log⁡(x+e)acos⁡(x)−1log⁡(log⁡(x+e))+e1−x2log⁡(x+e)log⁡(x+e)acos⁡(x)−1log⁡(log⁡(x+e))−log⁡(x+e)acos⁡(x)−1acos⁡(x)(x+e)(x2−1)\frac{x^{2} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)} - 1} \operatorname{acos}{\left(x \right)} + x \sqrt{1 - x^{2}} \log{\left(x + e \right)} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)} - 1} \log{\left(\log{\left(x + e \right)} \right)} + e \sqrt{1 - x^{2}} \log{\left(x + e \right)} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)} - 1} \log{\left(\log{\left(x + e \right)} \right)} - \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)} - 1} \operatorname{acos}{\left(x \right)}}{\left(x + e\right) \left(x^{2} - 1\right)} 
(-log(E + x)^(-1 + acos(x))*acos(x) + x^2*log(E + x)^(-1 + acos(x))*acos(x) + E*sqrt(1 - x^2)*log(E + x)^(-1 + acos(x))*log(E + x)*log(log(E + x)) + x*sqrt(1 - x^2)*log(E + x)^(-1 + acos(x))*log(E + x)*log(log(E + x)))/((-1 + x^2)*(E + x))
Denominador común [src] 
 /     ________                                                                                                                            \ 
 |    /      2     acos(x)                       acos(x)                                          acos(x)                                  | 
-\- \/  1 - x  *log       (E + x)*acos(x) + E*log       (E + x)*log(E + x)*log(log(E + x)) + x*log       (E + x)*log(E + x)*log(log(E + x))/ 
---------------------------------------------------------------------------------------------------------------------------------------------
                                                  ________                   ________                                                        
                                                 /      2                   /      2                                                         
                                             E*\/  1 - x  *log(E + x) + x*\/  1 - x  *log(E + x)
−xlog⁡(x+e)log⁡(x+e)acos⁡(x)log⁡(log⁡(x+e))−1−x2log⁡(x+e)acos⁡(x)acos⁡(x)+elog⁡(x+e)log⁡(x+e)acos⁡(x)log⁡(log⁡(x+e))x1−x2log⁡(x+e)+e1−x2log⁡(x+e)- \frac{x \log{\left(x + e \right)} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} \log{\left(\log{\left(x + e \right)} \right)} - \sqrt{1 - x^{2}} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} \operatorname{acos}{\left(x \right)} + e \log{\left(x + e \right)} \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} \log{\left(\log{\left(x + e \right)} \right)}}{x \sqrt{1 - x^{2}} \log{\left(x + e \right)} + e \sqrt{1 - x^{2}} \log{\left(x + e \right)}} 
-(-sqrt(1 - x^2)*log(E + x)^acos(x)*acos(x) + E*log(E + x)^acos(x)*log(E + x)*log(log(E + x)) + x*log(E + x)^acos(x)*log(E + x)*log(log(E + x)))/(E*sqrt(1 - x^2)*log(E + x) + x*sqrt(1 - x^2)*log(E + x))
Unión de expresiones racionales [src] 
                  /   ________                                             \
   acos(x)        |  /      2                                              |
log       (E + x)*\\/  1 - x  *acos(x) - (E + x)*log(E + x)*log(log(E + x))/
----------------------------------------------------------------------------
                          ________                                          
                         /      2                                           
                       \/  1 - x  *(E + x)*log(E + x)
(1−x2acos⁡(x)−(x+e)log⁡(x+e)log⁡(log⁡(x+e)))log⁡(x+e)acos⁡(x)1−x2(x+e)log⁡(x+e)\frac{\left(\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} - \left(x + e\right) \log{\left(x + e \right)} \log{\left(\log{\left(x + e \right)} \right)}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}}}{\sqrt{1 - x^{2}} \left(x + e\right) \log{\left(x + e \right)}} 
log(E + x)^acos(x)*(sqrt(1 - x^2)*acos(x) - (E + x)*log(E + x)*log(log(E + x)))/(sqrt(1 - x^2)*(E + x)*log(E + x))
Combinatoria [src] 
                   /     ________                                                                      \ 
    acos(x)        |    /      2                                                                       | 
-log       (E + x)*\- \/  1 - x  *acos(x) + E*log(E + x)*log(log(E + x)) + x*log(E + x)*log(log(E + x))/ 
---------------------------------------------------------------------------------------------------------
                                   ___________________                                                   
                                 \/ -(1 + x)*(-1 + x) *(E + x)*log(E + x)
−(xlog⁡(x+e)log⁡(log⁡(x+e))−1−x2acos⁡(x)+elog⁡(x+e)log⁡(log⁡(x+e)))log⁡(x+e)acos⁡(x)−(x−1)(x+1)(x+e)log⁡(x+e)- \frac{\left(x \log{\left(x + e \right)} \log{\left(\log{\left(x + e \right)} \right)} - \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} + e \log{\left(x + e \right)} \log{\left(\log{\left(x + e \right)} \right)}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(x + e\right) \log{\left(x + e \right)}} 
-log(E + x)^acos(x)*(-sqrt(1 - x^2)*acos(x) + E*log(E + x)*log(log(E + x)) + x*log(E + x)*log(log(E + x)))/(sqrt(-(1 + x)*(-1 + x))*(E + x)*log(E + x))
Potencias [src] 
   acos(x)        /  log(log(E + x))        acos(x)      \
log       (E + x)*|- --------------- + ------------------|
                  |       ________     (E + x)*log(E + x)|
                  |      /      2                        |
                  \    \/  1 - x                         /
(acos⁡(x)(x+e)log⁡(x+e)−log⁡(log⁡(x+e))1−x2)log⁡(x+e)acos⁡(x)\left(\frac{\operatorname{acos}{\left(x \right)}}{\left(x + e\right) \log{\left(x + e \right)}} - \frac{\log{\left(\log{\left(x + e \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} 
log(E + x)^acos(x)*(-log(log(E + x))/sqrt(1 - x^2) + acos(x)/((E + x)*log(E + x)))
Compilar la expresión [src] 
   acos(x)        /  log(log(x + E))        acos(x)      \
log       (x + E)*|- --------------- + ------------------|
                  |       ________     (E + x)*log(x + E)|
                  |      /      2                        |
                  \    \/  1 - x                         /
(acos⁡(x)(x+e)log⁡(x+e)−log⁡(log⁡(x+e))1−x2)log⁡(x+e)acos⁡(x)\left(\frac{\operatorname{acos}{\left(x \right)}}{\left(x + e\right) \log{\left(x + e \right)}} - \frac{\log{\left(\log{\left(x + e \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} 
   acos(x)        /  log(log(E + x))        acos(x)      \
log       (E + x)*|- --------------- + ------------------|
                  |       ________     (E + x)*log(E + x)|
                  |      /      2                        |
                  \    \/  1 - x                         /
(acos⁡(x)(x+e)log⁡(x+e)−log⁡(log⁡(x+e))1−x2)log⁡(x+e)acos⁡(x)\left(\frac{\operatorname{acos}{\left(x \right)}}{\left(x + e\right) \log{\left(x + e \right)}} - \frac{\log{\left(\log{\left(x + e \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} 
log(E + x)^acos(x)*(-log(log(E + x))/sqrt(1 - x^2) + acos(x)/((E + x)*log(E + x)))
Abrimos la expresión [src] 
   acos(x)        /-log(log(x + E))         acos(x)      \
log       (x + E)*|----------------- + ------------------|
                  |      ________      (x + E)*log(x + E)|
                  |     /      2                         |
                  \   \/  1 - x                          /
(acos⁡(x)(x+e)log⁡(x+e)+(−1)log⁡(log⁡(x+e))1−x2)log⁡(x+e)acos⁡(x)\left(\frac{\operatorname{acos}{\left(x \right)}}{\left(x + e\right) \log{\left(x + e \right)}} + \frac{\left(-1\right) \log{\left(\log{\left(x + e \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} 
log(x + E)^acos(x)*((-log(log(x + E)))/sqrt(1 - x^2) + acos(x)/((x + E)*log(x + E)))
Parte trigonométrica [src] 
   acos(x)        /  log(log(E + x))        acos(x)      \
log       (E + x)*|- --------------- + ------------------|
                  |       ________     (E + x)*log(E + x)|
                  |      /      2                        |
                  \    \/  1 - x                         /
(acos⁡(x)(x+e)log⁡(x+e)−log⁡(log⁡(x+e))1−x2)log⁡(x+e)acos⁡(x)\left(\frac{\operatorname{acos}{\left(x \right)}}{\left(x + e\right) \log{\left(x + e \right)}} - \frac{\log{\left(\log{\left(x + e \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x + e \right)}^{\operatorname{acos}{\left(x \right)}} 
   acos(x)                        /  log(log(x + cosh(1) + sinh(1)))                        acos(x)                      \
log       (x + cosh(1) + sinh(1))*|- ------------------------------- + --------------------------------------------------|
                                  |               ________             (x + cosh(1) + sinh(1))*log(x + cosh(1) + sinh(1))|
                                  |              /      2                                                                |
                                  \            \/  1 - x                                                                 /
(acos⁡(x)(x+sinh⁡(1)+cosh⁡(1))log⁡(x+sinh⁡(1)+cosh⁡(1))−log⁡(log⁡(x+sinh⁡(1)+cosh⁡(1)))1−x2)log⁡(x+sinh⁡(1)+cosh⁡(1))acos⁡(x)\left(\frac{\operatorname{acos}{\left(x \right)}}{\left(x + \sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right) \log{\left(x + \sinh{\left(1 \right)} + \cosh{\left(1 \right)} \right)}} - \frac{\log{\left(\log{\left(x + \sinh{\left(1 \right)} + \cosh{\left(1 \right)} \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x + \sinh{\left(1 \right)} + \cosh{\left(1 \right)} \right)}^{\operatorname{acos}{\left(x \right)}} 
log(x + cosh(1) + sinh(1))^acos(x)*(-log(log(x + cosh(1) + sinh(1)))/sqrt(1 - x^2) + acos(x)/((x + cosh(1) + sinh(1))*log(x + cosh(1) + sinh(1))))
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