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

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

Expresión a simplificar:

Solución

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