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Descomponer al cuadrado:
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Expresiones idénticas
asin(x)^ dos *(log(x+ uno)/ cuatro -log(x- uno)/ cuatro -x/(dos *x^ dos - dos))
ar coseno de eno de (x) al cuadrado multiplicar por ( logaritmo de (x más 1) dividir por 4 menos logaritmo de (x menos 1) dividir por 4 menos x dividir por (2 multiplicar por x al cuadrado menos 2))
ar coseno de eno de (x) en el grado dos multiplicar por ( logaritmo de (x más uno) dividir por cuatro menos logaritmo de (x menos uno) dividir por cuatro menos x dividir por (dos multiplicar por x en el grado dos menos dos))
asin(x)2*(log(x+1)/4-log(x-1)/4-x/(2*x2-2))
asinx2*logx+1/4-logx-1/4-x/2*x2-2
asin(x)²*(log(x+1)/4-log(x-1)/4-x/(2*x²-2))
asin(x) en el grado 2*(log(x+1)/4-log(x-1)/4-x/(2*x en el grado 2-2))
asin(x)^2(log(x+1)/4-log(x-1)/4-x/(2x^2-2))
asin(x)2(log(x+1)/4-log(x-1)/4-x/(2x2-2))
asinx2logx+1/4-logx-1/4-x/2x2-2
asinx^2logx+1/4-logx-1/4-x/2x^2-2
asin(x)^2*(log(x+1) dividir por 4-log(x-1) dividir por 4-x dividir por (2*x^2-2))
Expresiones semejantes
asin(x)^2*(log(x+1)/4-log(x-1)/4+x/(2*x^2-2))
asin(x)^2*(log(x+1)/4+log(x-1)/4-x/(2*x^2-2))
asin(x)^2*(log(x+1)/4-log(x+1)/4-x/(2*x^2-2))
asin(x)^2*(log(x-1)/4-log(x-1)/4-x/(2*x^2-2))
asin(x)^2*(log(x+1)/4-log(x-1)/4-x/(2*x^2+2))
arcsin(x)^2*(log(x+1)/4-log(x-1)/4-x/(2*x^2-2))
arcsinx^2*(log(x+1)/4-log(x-1)/4-x/(2*x^2-2))
Expresiones con funciones
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asin(x/sqrt(1+x^2))^2*(1/(sqrt(1+x^2))-x^2/(1+x^2)^(3/2))/sqrt(1-x^2/(1+x^2))
asin(sqrt(x))+(x-(1/2))/(2*sqrt(x-x^2))-x/(2*sqrt(x-x^2))
asinh((8*x-4)/(4*sqrt(6)))/2
asin(x/(sqrt(6)*|x+2|)+7/(sqrt(6)*|x+2|))/5^(3/2)+sqrt(x^2+2*x-5)/(10+5*x)
asinh((8*x-1)/(3*sqrt(7)))/2
Logaritmo log
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log(x+9)/81-log(x)/81-1/(9*x)
log(x^2+x-1)/2-log((2*x-sqrt(5)+1)/(1+sqrt(5)+2*x))/(2*sqrt(5))
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Logaritmo log
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log(x^2+x-1)/2-log((2*x-sqrt(5)+1)/(1+sqrt(5)+2*x))/(2*sqrt(5))
log(x)/log(5)/5*((x+exp(-x)*x)^(1/5))+(x+5)/(2*sin(x)+x)
log(x^2+1)/2-log(x)+atan(x)/2+(x-2)/(2+2*x^2)

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

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

Solución

Ha introducido [src]

    2    /log(x + 1)   log(x - 1)      x    \
asin (x)*|---------- - ---------- - --------|
         |    4            4           2    |
         \                          2*x  - 2/

$$\left(- \frac{x}{2 x^{2} - 2} + \left(- \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4}\right)\right) \operatorname{asin}^{2}{\left(x \right)}$$

asin(x)^2*(log(x + 1)/4 - log(x - 1)/4 - x/(2*x^2 - 2))

Simplificación general [src]

     2    /      /      2\                            \ 
-asin (x)*\2*x + \-1 + x /*(-log(1 + x) + log(-1 + x))/ 
--------------------------------------------------------
                               2                        
                       -4 + 4*x

$$- \frac{\left(2 x + \left(x^{2} - 1\right) \left(\log{\left(x - 1 \right)} - \log{\left(x + 1 \right)}\right)\right) \operatorname{asin}^{2}{\left(x \right)}}{4 x^{2} - 4}$$

-asin(x)^2*(2*x + (-1 + x^2)*(-log(1 + x) + log(-1 + x)))/(-4 + 4*x^2)

Respuesta numérica [src]

asin(x)^2*(0.25*log(x + 1) - 0.25*log(x - 1) - x/(-2.0 + 2.0*x^2))

asin(x)^2*(0.25*log(x + 1) - 0.25*log(x - 1) - x/(-2.0 + 2.0*x^2))

Parte trigonométrica [src]

    2    /  log(-1 + x)   log(1 + x)       x    \
asin (x)*|- ----------- + ---------- - ---------|
         |       4            4                2|
         \                             -2 + 2*x /

$$\left(- \frac{x}{2 x^{2} - 2} - \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4}\right) \operatorname{asin}^{2}{\left(x \right)}$$

asin(x)^2*(-log(-1 + x)/4 + log(1 + x)/4 - x/(-2 + 2*x^2))

Denominador racional [src]

     2    /                      2                2                        \ 
-asin (x)*\-log(-1 + x) + 2*x + x *log(-1 + x) - x *log(1 + x) + log(1 + x)/ 
-----------------------------------------------------------------------------
                                          2                                  
                                  -4 + 4*x

$$- \frac{\left(x^{2} \log{\left(x - 1 \right)} - x^{2} \log{\left(x + 1 \right)} + 2 x - \log{\left(x - 1 \right)} + \log{\left(x + 1 \right)}\right) \operatorname{asin}^{2}{\left(x \right)}}{4 x^{2} - 4}$$

-asin(x)^2*(-log(-1 + x) + 2*x + x^2*log(-1 + x) - x^2*log(1 + x) + log(1 + x))/(-4 + 4*x^2)

Potencias [src]

    2    /  log(-1 + x)   log(1 + x)       x    \
asin (x)*|- ----------- + ---------- - ---------|
         |       4            4                2|
         \                             -2 + 2*x /

$$\left(- \frac{x}{2 x^{2} - 2} - \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4}\right) \operatorname{asin}^{2}{\left(x \right)}$$

asin(x)^2*(-log(-1 + x)/4 + log(1 + x)/4 - x/(-2 + 2*x^2))

Combinatoria [src]

    2    /                     2               2                          \
asin (x)*\-log(1 + x) - 2*x + x *log(1 + x) - x *log(-1 + x) + log(-1 + x)/
---------------------------------------------------------------------------
                             4*(1 + x)*(-1 + x)

$$\frac{\left(- x^{2} \log{\left(x - 1 \right)} + x^{2} \log{\left(x + 1 \right)} - 2 x + \log{\left(x - 1 \right)} - \log{\left(x + 1 \right)}\right) \operatorname{asin}^{2}{\left(x \right)}}{4 \left(x - 1\right) \left(x + 1\right)}$$

asin(x)^2*(-log(1 + x) - 2*x + x^2*log(1 + x) - x^2*log(-1 + x) + log(-1 + x))/(4*(1 + x)*(-1 + x))

Denominador común [src]

      2                      2                       2   
  asin (x)*log(-1 + x)   asin (x)*log(1 + x)   x*asin (x)
- -------------------- + ------------------- - ----------
           4                      4                    2 
                                               -2 + 2*x

$$- \frac{x \operatorname{asin}^{2}{\left(x \right)}}{2 x^{2} - 2} - \frac{\log{\left(x - 1 \right)} \operatorname{asin}^{2}{\left(x \right)}}{4} + \frac{\log{\left(x + 1 \right)} \operatorname{asin}^{2}{\left(x \right)}}{4}$$

-asin(x)^2*log(-1 + x)/4 + asin(x)^2*log(1 + x)/4 - x*asin(x)^2/(-2 + 2*x^2)

Unión de expresiones racionales [src]

    2    /       /      2\                            \
asin (x)*\-2*x + \-1 + x /*(-log(-1 + x) + log(1 + x))/
-------------------------------------------------------
                        /      2\                      
                      4*\-1 + x /

$$\frac{\left(- 2 x + \left(x^{2} - 1\right) \left(- \log{\left(x - 1 \right)} + \log{\left(x + 1 \right)}\right)\right) \operatorname{asin}^{2}{\left(x \right)}}{4 \left(x^{2} - 1\right)}$$

asin(x)^2*(-2*x + (-1 + x^2)*(-log(-1 + x) + log(1 + x)))/(4*(-1 + x^2))

Compilar la expresión [src]

    2    /  log(x - 1)   log(x + 1)       x    \
asin (x)*|- ---------- + ---------- - ---------|
         |      4            4                2|
         \                            -2 + 2*x /

$$\left(- \frac{x}{2 x^{2} - 2} - \frac{\log{\left(x - 1 \right)}}{4} + \frac{\log{\left(x + 1 \right)}}{4}\right) \operatorname{asin}^{2}{\left(x \right)}$$

asin(x)^2*(-log(x - 1)/4 + log(x + 1)/4 - x/(-2 + 2*x^2))

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

Solución

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