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Simplificación de expresiones/ Descomposición en fracciones simples/ acos(x)^4*(1+2*x)/(x^2+x-1)-4*acos(x)^3*log(x^2+x-1)/sqrt(1-x^2)

¿Cómo vas a descomponer esta acos(x)^4*(1+2*x)/(x^2+x-1)-4*acos(x)^3*log(x^2+x-1)/sqrt(1-x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    4                      3       / 2        \
acos (x)*(1 + 2*x)   4*acos (x)*log\x  + x - 1/
------------------ - --------------------------
     2                         ________        
    x  + x - 1                /      2         
                            \/  1 - x
(2x+1)acos⁡4(x)(x2+x)−1−log⁡((x2+x)−1)4acos⁡3(x)1−x2\frac{\left(2 x + 1\right) \operatorname{acos}^{4}{\left(x \right)}}{\left(x^{2} + x\right) - 1} - \frac{\log{\left(\left(x^{2} + x\right) - 1 \right)} 4 \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}} 
(acos(x)^4*(1 + 2*x))/(x^2 + x - 1) - (4*acos(x)^3)*log(x^2 + x - 1)/sqrt(1 - x^2)
Simplificación general [src] 
         /                                        ________                  \
    3    |    /          2\    /          2\     /      2                   |
acos (x)*\- 4*\-1 + x + x /*log\-1 + x + x / + \/  1 - x  *(1 + 2*x)*acos(x)/
-----------------------------------------------------------------------------
                             ________                                        
                            /      2  /          2\                          
                          \/  1 - x  *\-1 + x + x /
(1−x2(2x+1)acos⁡(x)−4(x2+x−1)log⁡(x2+x−1))acos⁡3(x)1−x2(x2+x−1)\frac{\left(\sqrt{1 - x^{2}} \left(2 x + 1\right) \operatorname{acos}{\left(x \right)} - 4 \left(x^{2} + x - 1\right) \log{\left(x^{2} + x - 1 \right)}\right) \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x^{2} + x - 1\right)} 
acos(x)^3*(-4*(-1 + x + x^2)*log(-1 + x + x^2) + sqrt(1 - x^2)*(1 + 2*x)*acos(x))/(sqrt(1 - x^2)*(-1 + x + x^2))
Parte trigonométrica [src] 
    4                      3       /          2\
acos (x)*(1 + 2*x)   4*acos (x)*log\-1 + x + x /
------------------ - ---------------------------
             2                  ________        
   -1 + x + x                  /      2         
                             \/  1 - x
(2x+1)acos⁡4(x)x2+x−1−4log⁡(x2+x−1)acos⁡3(x)1−x2\frac{\left(2 x + 1\right) \operatorname{acos}^{4}{\left(x \right)}}{x^{2} + x - 1} - \frac{4 \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}} 
acos(x)^4*(1 + 2*x)/(-1 + x + x^2) - 4*acos(x)^3*log(-1 + x + x^2)/sqrt(1 - x^2)
Potencias [src] 
    4                      3       /          2\
acos (x)*(1 + 2*x)   4*acos (x)*log\-1 + x + x /
------------------ - ---------------------------
             2                  ________        
   -1 + x + x                  /      2         
                             \/  1 - x
(2x+1)acos⁡4(x)x2+x−1−4log⁡(x2+x−1)acos⁡3(x)1−x2\frac{\left(2 x + 1\right) \operatorname{acos}^{4}{\left(x \right)}}{x^{2} + x - 1} - \frac{4 \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}} 
acos(x)^4*(1 + 2*x)/(-1 + x + x^2) - 4*acos(x)^3*log(-1 + x + x^2)/sqrt(1 - x^2)
Unión de expresiones racionales [src] 
         /                                             ________                  \
    3    |                                            /      2                   |
acos (x)*\-4*(-1 + x*(1 + x))*log(-1 + x*(1 + x)) + \/  1 - x  *(1 + 2*x)*acos(x)/
----------------------------------------------------------------------------------
                              ________                                            
                             /      2                                             
                           \/  1 - x  *(-1 + x*(1 + x))
(1−x2(2x+1)acos⁡(x)−4(x(x+1)−1)log⁡(x(x+1)−1))acos⁡3(x)1−x2(x(x+1)−1)\frac{\left(\sqrt{1 - x^{2}} \left(2 x + 1\right) \operatorname{acos}{\left(x \right)} - 4 \left(x \left(x + 1\right) - 1\right) \log{\left(x \left(x + 1\right) - 1 \right)}\right) \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}} \left(x \left(x + 1\right) - 1\right)} 
acos(x)^3*(-4*(-1 + x*(1 + x))*log(-1 + x*(1 + x)) + sqrt(1 - x^2)*(1 + 2*x)*acos(x))/(sqrt(1 - x^2)*(-1 + x*(1 + x)))
Combinatoria [src] 
          /                          ________                                                                 ________        \ 
     3    |       /          2\     /      2                   /          2\      2    /          2\         /      2         | 
-acos (x)*\- 4*log\-1 + x + x / - \/  1 - x  *acos(x) + 4*x*log\-1 + x + x / + 4*x *log\-1 + x + x / - 2*x*\/  1 - x  *acos(x)/ 
--------------------------------------------------------------------------------------------------------------------------------
                                                ___________________ /          2\                                               
                                              \/ -(1 + x)*(-1 + x) *\-1 + x + x /
−(4x2log⁡(x2+x−1)−2x1−x2acos⁡(x)+4xlog⁡(x2+x−1)−1−x2acos⁡(x)−4log⁡(x2+x−1))acos⁡3(x)−(x−1)(x+1)(x2+x−1)- \frac{\left(4 x^{2} \log{\left(x^{2} + x - 1 \right)} - 2 x \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} + 4 x \log{\left(x^{2} + x - 1 \right)} - \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)} - 4 \log{\left(x^{2} + x - 1 \right)}\right) \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + x - 1\right)} 
-acos(x)^3*(-4*log(-1 + x + x^2) - sqrt(1 - x^2)*acos(x) + 4*x*log(-1 + x + x^2) + 4*x^2*log(-1 + x + x^2) - 2*x*sqrt(1 - x^2)*acos(x))/(sqrt(-(1 + x)*(-1 + x))*(-1 + x + x^2))
Denominador común [src] 
 /     ________                                                 ________                                                                          \ 
 |    /      2      4            3       /          2\         /      2      4              3       /          2\      2     3       /          2\| 
-\- \/  1 - x  *acos (x) - 4*acos (x)*log\-1 + x + x / - 2*x*\/  1 - x  *acos (x) + 4*x*acos (x)*log\-1 + x + x / + 4*x *acos (x)*log\-1 + x + x // 
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                                                        ________        ________         ________                                                   
                                                       /      2        /      2     2   /      2                                                    
                                                   - \/  1 - x   + x*\/  1 - x   + x *\/  1 - x
−4x2log⁡(x2+x−1)acos⁡3(x)−2x1−x2acos⁡4(x)+4xlog⁡(x2+x−1)acos⁡3(x)−1−x2acos⁡4(x)−4log⁡(x2+x−1)acos⁡3(x)x21−x2+x1−x2−1−x2- \frac{4 x^{2} \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)} - 2 x \sqrt{1 - x^{2}} \operatorname{acos}^{4}{\left(x \right)} + 4 x \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)} - \sqrt{1 - x^{2}} \operatorname{acos}^{4}{\left(x \right)} - 4 \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}} + x \sqrt{1 - x^{2}} - \sqrt{1 - x^{2}}} 
-(-sqrt(1 - x^2)*acos(x)^4 - 4*acos(x)^3*log(-1 + x + x^2) - 2*x*sqrt(1 - x^2)*acos(x)^4 + 4*x*acos(x)^3*log(-1 + x + x^2) + 4*x^2*acos(x)^3*log(-1 + x + x^2))/(-sqrt(1 - x^2) + x*sqrt(1 - x^2) + x^2*sqrt(1 - x^2))
Compilar la expresión [src] 
    4                      3       / 2        \
acos (x)*(1 + 2*x)   4*acos (x)*log\x  + x - 1/
------------------ - --------------------------
             2                 ________        
   -1 + x + x                 /      2         
                            \/  1 - x
(2x+1)acos⁡4(x)x2+x−1−4log⁡((x2+x)−1)acos⁡3(x)1−x2\frac{\left(2 x + 1\right) \operatorname{acos}^{4}{\left(x \right)}}{x^{2} + x - 1} - \frac{4 \log{\left(\left(x^{2} + x\right) - 1 \right)} \operatorname{acos}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}} 
acos(x)^4*(1 + 2*x)/(-1 + x + x^2) - 4*acos(x)^3*log(x^2 + x - 1)/sqrt(1 - x^2)
Denominador racional [src] 
                                                               ________                                    ________                                     ________                          
      4       2     4              4         3     4          /      2      3       /          2\         /      2      3       /          2\      2   /      2      3       /          2\
- acos (x) + x *acos (x) - 2*x*acos (x) + 2*x *acos (x) - 4*\/  1 - x  *acos (x)*log\-1 + x + x / + 4*x*\/  1 - x  *acos (x)*log\-1 + x + x / + 4*x *\/  1 - x  *acos (x)*log\-1 + x + x /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                 /      2\ /          2\                                                                                  
                                                                                 \-1 + x /*\-1 + x + x /
2x3acos⁡4(x)+4x21−x2log⁡(x2+x−1)acos⁡3(x)+x2acos⁡4(x)+4x1−x2log⁡(x2+x−1)acos⁡3(x)−2xacos⁡4(x)−41−x2log⁡(x2+x−1)acos⁡3(x)−acos⁡4(x)(x2−1)(x2+x−1)\frac{2 x^{3} \operatorname{acos}^{4}{\left(x \right)} + 4 x^{2} \sqrt{1 - x^{2}} \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)} + x^{2} \operatorname{acos}^{4}{\left(x \right)} + 4 x \sqrt{1 - x^{2}} \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)} - 2 x \operatorname{acos}^{4}{\left(x \right)} - 4 \sqrt{1 - x^{2}} \log{\left(x^{2} + x - 1 \right)} \operatorname{acos}^{3}{\left(x \right)} - \operatorname{acos}^{4}{\left(x \right)}}{\left(x^{2} - 1\right) \left(x^{2} + x - 1\right)} 
(-acos(x)^4 + x^2*acos(x)^4 - 2*x*acos(x)^4 + 2*x^3*acos(x)^4 - 4*sqrt(1 - x^2)*acos(x)^3*log(-1 + x + x^2) + 4*x*sqrt(1 - x^2)*acos(x)^3*log(-1 + x + x^2) + 4*x^2*sqrt(1 - x^2)*acos(x)^3*log(-1 + x + x^2))/((-1 + x^2)*(-1 + x + x^2))
Respuesta numérica [src] 
acos(x)^4*(1.0 + 2.0*x)/(-1.0 + x + x^2) - 4.0*(1.0 - x^2)^(-0.5)*acos(x)^3*log(x^2 + x - 1)
acos(x)^4*(1.0 + 2.0*x)/(-1.0 + x + x^2) - 4.0*(1.0 - x^2)^(-0.5)*acos(x)^3*log(x^2 + x - 1)
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