Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ asin(x)/(1-x^2)^(3/2)+3*x/(-1+x^2)^2+3*x^2*asin(x)/(1-x^2)^(5/2)

¿Cómo vas a descomponer esta asin(x)/(1-x^2)^(3/2)+3*x/(-1+x^2)^2+3*x^2*asin(x)/(1-x^2)^(5/2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                              2        
  asin(x)        3*x       3*x *asin(x)
----------- + ---------- + ------------
        3/2            2           5/2 
/     2\      /      2\    /     2\    
\1 - x /      \-1 + x /    \1 - x /
3x2asin⁡(x)(1−x2)52+(3x(x2−1)2+asin⁡(x)(1−x2)32)\frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \left(\frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) 
asin(x)/(1 - x^2)^(3/2) + (3*x)/(-1 + x^2)^2 + ((3*x^2)*asin(x))/(1 - x^2)^(5/2)
Simplificación general [src] 
        9/2                       4                7/2        
/     2\                  /     2\       2 /     2\           
\1 - x /   *asin(x) + 3*x*\1 - x /  + 3*x *\1 - x /   *asin(x)
--------------------------------------------------------------
                                   6                          
                          /      2\                           
                          \-1 + x /
3x2(1−x2)72asin⁡(x)+3x(1−x2)4+(1−x2)92asin⁡(x)(x2−1)6\frac{3 x^{2} \left(1 - x^{2}\right)^{\frac{7}{2}} \operatorname{asin}{\left(x \right)} + 3 x \left(1 - x^{2}\right)^{4} + \left(1 - x^{2}\right)^{\frac{9}{2}} \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{6}} 
((1 - x^2)^(9/2)*asin(x) + 3*x*(1 - x^2)^4 + 3*x^2*(1 - x^2)^(7/2)*asin(x))/(-1 + x^2)^6
Compilar la expresión [src] 
                              2        
  asin(x)        3*x       3*x *asin(x)
----------- + ---------- + ------------
        3/2            2           5/2 
/     2\      /      2\    /     2\    
\1 - x /      \-1 + x /    \1 - x /
3x2asin⁡(x)(1−x2)52+3x(x2−1)2+asin⁡(x)(1−x2)32\frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} 
asin(x)/(1 - x^2)^(3/2) + 3*x/(-1 + x^2)^2 + 3*x^2*asin(x)/(1 - x^2)^(5/2)
Denominador racional [src] 
        5/2 /         2                       3/2\                3/2          2        
/     2\    |/      2\                /     2\   |      2 /     2\    /      2\         
\1 - x /   *\\-1 + x / *asin(x) + 3*x*\1 - x /   / + 3*x *\1 - x /   *\-1 + x / *asin(x)
----------------------------------------------------------------------------------------
                                          4          2                                  
                                  /     2\  /      2\                                   
                                  \1 - x / *\-1 + x /
3x2(1−x2)32(x2−1)2asin⁡(x)+(1−x2)52(3x(1−x2)32+(x2−1)2asin⁡(x))(1−x2)4(x2−1)2\frac{3 x^{2} \left(1 - x^{2}\right)^{\frac{3}{2}} \left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)} + \left(1 - x^{2}\right)^{\frac{5}{2}} \left(3 x \left(1 - x^{2}\right)^{\frac{3}{2}} + \left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}\right)}{\left(1 - x^{2}\right)^{4} \left(x^{2} - 1\right)^{2}} 
((1 - x^2)^(5/2)*((-1 + x^2)^2*asin(x) + 3*x*(1 - x^2)^(3/2)) + 3*x^2*(1 - x^2)^(3/2)*(-1 + x^2)^2*asin(x))/((1 - x^2)^4*(-1 + x^2)^2)
Respuesta numérica [src] 
(1.0 - x^2)^(-1.5)*asin(x) + 3.0*x/(-1.0 + x^2)^2 + 3.0*x^2*(1.0 - x^2)^(-2.5)*asin(x)
(1.0 - x^2)^(-1.5)*asin(x) + 3.0*x/(-1.0 + x^2)^2 + 3.0*x^2*(1.0 - x^2)^(-2.5)*asin(x)
Denominador común [src] 
                 ________                   ________        
          3     /      2               2   /      2         
-3*x + 3*x  - \/  1 - x  *asin(x) - 2*x *\/  1 - x  *asin(x)
------------------------------------------------------------
                         6      4      2                    
                   -1 + x  - 3*x  + 3*x
3x3−2x21−x2asin⁡(x)−3x−1−x2asin⁡(x)x6−3x4+3x2−1\frac{3 x^{3} - 2 x^{2} \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)} - 3 x - \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{x^{6} - 3 x^{4} + 3 x^{2} - 1} 
(-3*x + 3*x^3 - sqrt(1 - x^2)*asin(x) - 2*x^2*sqrt(1 - x^2)*asin(x))/(-1 + x^6 - 3*x^4 + 3*x^2)
Potencias [src] 
                              2        
  asin(x)        3*x       3*x *asin(x)
----------- + ---------- + ------------
        3/2            2           5/2 
/     2\      /      2\    /     2\    
\1 - x /      \-1 + x /    \1 - x /
3x2asin⁡(x)(1−x2)52+3x(x2−1)2+asin⁡(x)(1−x2)32\frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} 
asin(x)/(1 - x^2)^(3/2) + 3*x/(-1 + x^2)^2 + 3*x^2*asin(x)/(1 - x^2)^(5/2)
Parte trigonométrica [src] 
                              2        
  asin(x)        3*x       3*x *asin(x)
----------- + ---------- + ------------
        3/2            2           5/2 
/     2\      /      2\    /     2\    
\1 - x /      \-1 + x /    \1 - x /
3x2asin⁡(x)(1−x2)52+3x(x2−1)2+asin⁡(x)(1−x2)32\frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} 
asin(x)/(1 - x^2)^(3/2) + 3*x/(-1 + x^2)^2 + 3*x^2*asin(x)/(1 - x^2)^(5/2)
Unión de expresiones racionales [src] 
         /         2                       3/2\                 2        
/     2\ |/      2\                /     2\   |      2 /      2\         
\1 - x /*\\-1 + x / *asin(x) + 3*x*\1 - x /   / + 3*x *\-1 + x / *asin(x)
-------------------------------------------------------------------------
                                  5/2          2                         
                          /     2\    /      2\                          
                          \1 - x /   *\-1 + x /
3x2(x2−1)2asin⁡(x)+(1−x2)(3x(1−x2)32+(x2−1)2asin⁡(x))(1−x2)52(x2−1)2\frac{3 x^{2} \left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)} + \left(1 - x^{2}\right) \left(3 x \left(1 - x^{2}\right)^{\frac{3}{2}} + \left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}\right)}{\left(1 - x^{2}\right)^{\frac{5}{2}} \left(x^{2} - 1\right)^{2}} 
((1 - x^2)*((-1 + x^2)^2*asin(x) + 3*x*(1 - x^2)^(3/2)) + 3*x^2*(-1 + x^2)^2*asin(x))/((1 - x^2)^(5/2)*(-1 + x^2)^2)
Combinatoria [src] 
                      ________          
   2                 /      2           
2*x *asin(x) + 3*x*\/  1 - x   + asin(x)
----------------------------------------
                            5/2         
         (-(1 + x)*(-1 + x))
2x2asin⁡(x)+3x1−x2+asin⁡(x)(−(x−1)(x+1))52\frac{2 x^{2} \operatorname{asin}{\left(x \right)} + 3 x \sqrt{1 - x^{2}} + \operatorname{asin}{\left(x \right)}}{\left(- \left(x - 1\right) \left(x + 1\right)\right)^{\frac{5}{2}}} 
(2*x^2*asin(x) + 3*x*sqrt(1 - x^2) + asin(x))/(-(1 + x)*(-1 + x))^(5/2)
    © Sr Examen – Калькулятор