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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                  /   ________            \
                  |  /      2             |
  asin(x)     3*x*\\/  1 - x   + x*asin(x)/
----------- + -----------------------------
        3/2                    5/2         
/     2\               /     2\            
\1 - x /               \1 - x /
3x(xasin⁡(x)+1−x2)(1−x2)52+asin⁡(x)(1−x2)32\frac{3 x \left(x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}\right)}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} 
asin(x)/(1 - x^2)^(3/2) + ((3*x)*(sqrt(1 - x^2) + x*asin(x)))/(1 - x^2)^(5/2)
Simplificación general [src] 
                       /   ________            \
/     2\               |  /      2             |
\1 - x /*asin(x) + 3*x*\\/  1 - x   + x*asin(x)/
------------------------------------------------
                          5/2                   
                  /     2\                      
                  \1 - x /
3x(xasin⁡(x)+1−x2)+(1−x2)asin⁡(x)(1−x2)52\frac{3 x \left(x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}\right) + \left(1 - x^{2}\right) \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} 
((1 - x^2)*asin(x) + 3*x*(sqrt(1 - x^2) + x*asin(x)))/(1 - x^2)^(5/2)
Respuesta numérica [src] 
(1.0 - x^2)^(-1.5)*asin(x) + 3.0*x*(1.0 - x^2)^(-2.5)*((1.0 - x^2)^0.5 + x*asin(x))
(1.0 - x^2)^(-1.5)*asin(x) + 3.0*x*(1.0 - x^2)^(-2.5)*((1.0 - x^2)^0.5 + x*asin(x))
Denominador común [src] 
                          ________             
       2                 /      2              
    2*x *asin(x) + 3*x*\/  1 - x   + asin(x)   
-----------------------------------------------
   ________         ________           ________
  /      2     4   /      2       2   /      2 
\/  1 - x   + x *\/  1 - x   - 2*x *\/  1 - x
2x2asin⁡(x)+3x1−x2+asin⁡(x)x41−x2−2x21−x2+1−x2\frac{2 x^{2} \operatorname{asin}{\left(x \right)} + 3 x \sqrt{1 - x^{2}} + \operatorname{asin}{\left(x \right)}}{x^{4} \sqrt{1 - x^{2}} - 2 x^{2} \sqrt{1 - x^{2}} + \sqrt{1 - x^{2}}} 
(2*x^2*asin(x) + 3*x*sqrt(1 - x^2) + asin(x))/(sqrt(1 - x^2) + x^4*sqrt(1 - x^2) - 2*x^2*sqrt(1 - x^2))
Denominador racional [src] 
        5/2                       3/2 /   ________            \
/     2\                  /     2\    |  /      2             |
\1 - x /   *asin(x) + 3*x*\1 - x /   *\\/  1 - x   + x*asin(x)/
---------------------------------------------------------------
                                   4                           
                           /     2\                            
                           \1 - x /
3x(1−x2)32(xasin⁡(x)+1−x2)+(1−x2)52asin⁡(x)(1−x2)4\frac{3 x \left(1 - x^{2}\right)^{\frac{3}{2}} \left(x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}\right) + \left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{4}} 
((1 - x^2)^(5/2)*asin(x) + 3*x*(1 - x^2)^(3/2)*(sqrt(1 - x^2) + x*asin(x)))/(1 - x^2)^4
Unión de expresiones racionales [src] 
                       /   ________            \
/     2\               |  /      2             |
\1 - x /*asin(x) + 3*x*\\/  1 - x   + x*asin(x)/
------------------------------------------------
                          5/2                   
                  /     2\                      
                  \1 - x /
3x(xasin⁡(x)+1−x2)+(1−x2)asin⁡(x)(1−x2)52\frac{3 x \left(x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}\right) + \left(1 - x^{2}\right) \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} 
((1 - x^2)*asin(x) + 3*x*(sqrt(1 - x^2) + x*asin(x)))/(1 - x^2)^(5/2)
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)
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