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Simplificación de expresiones/ Descomposición en fracciones simples/ Piecewise((-acosh(1/x)+1/(x*sqrt(-1+x^(-2)))-x/sqrt(-1+x^(-2)),1/|x^2|>1),(i*asin(1/x)+i*x/((sqrt(1/(x^2))*sqrt(1-1)))-i/(x*(sqrt(1/(x^2))*sqrt(1-1))),True))

¿Cómo vas a descomponer esta Piecewise((-acosh(1/x)+1/(x*sqrt(-1+x^(-2)))-x/sqrt(-1+x^(-2)),1/|x^2|>1),(i*asin(1/x)+i*x/((sqrt(1/(x^2))*sqrt(1-1)))-i/(x*(sqrt(1/(x^2))*sqrt(1-1))),True)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
/       /1\          1                 x              1      
|- acosh|-| + ---------------- - --------------  for ---- > 1
|       \x/          _________        _________      | 2|    
|                   /      1         /      1        |x |    
|             x*   /  -1 + --       /  -1 + --               
<                 /         2      /         2               
|               \/         x     \/         x                
|                                                            
|                       /1\                                  
|           zoo + I*asin|-| + zoo*x               otherwise  
\                       \x/
{−x−1+1x2−acosh⁡(1x)+1x−1+1x2for 1∣x2∣>1∞~x+iasin⁡(1x)+∞~otherwise\begin{cases} - \frac{x}{\sqrt{-1 + \frac{1}{x^{2}}}} - \operatorname{acosh}{\left(\frac{1}{x} \right)} + \frac{1}{x \sqrt{-1 + \frac{1}{x^{2}}}} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\\tilde{\infty} x + i \operatorname{asin}{\left(\frac{1}{x} \right)} + \tilde{\infty} & \text{otherwise} \end{cases} 
Piecewise((-acosh(1/x) + 1/(x*sqrt(-1 + x^(-2))) - x/sqrt(-1 + x^(-2)), 1/|x^2| > 1), (±oo + i*asin(1/x) + ±oo*x, True))
Simplificación general [src] 
/                    _________              
|       /1\         /      1         1      
|- acosh|-| + x*   /  -1 + --   for ---- > 1
|       \x/       /         2       | 2|    
<               \/         x        |x |    
|                                           
|               /1\                         
|   zoo + I*asin|-| + zoo*x      otherwise  
\               \x/
{x−1+1x2−acosh⁡(1x)for 1∣x2∣>1∞~x+iasin⁡(1x)+∞~otherwise\begin{cases} x \sqrt{-1 + \frac{1}{x^{2}}} - \operatorname{acosh}{\left(\frac{1}{x} \right)} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\\tilde{\infty} x + i \operatorname{asin}{\left(\frac{1}{x} \right)} + \tilde{\infty} & \text{otherwise} \end{cases} 
Piecewise((-acosh(1/x) + x*sqrt(-1 + x^(-2)), 1/|x^2| > 1), (±oo + i*asin(1/x) + ±oo*x, True))
Respuesta numérica [src] 
Piecewise((-acosh(1/x) + (-1.0 + x^(-2))^(-0.5)/x - x*(-1.0 + x^(-2))^(-0.5), 1/|x^2| > 1), (±oo + i*asin(1/x) + ±oo*x, True))
Piecewise((-acosh(1/x) + (-1.0 + x^(-2))^(-0.5)/x - x*(-1.0 + x^(-2))^(-0.5), 1/|x^2| > 1), (±oo + i*asin(1/x) + ±oo*x, True))
Unión de expresiones racionales [src] 
/                 ________                       
|                /      2                        
|     2         /  1 - x        /1\              
|1 - x  - x*   /   ------ *acosh|-|              
|             /       2         \x/              
|           \/       x                    1      
|----------------------------------  for ---- > 1
|                 ________               | 2|    
<                /      2                |x |    
|               /  1 - x                         
|         x*   /   ------                        
|             /       2                          
|           \/       x                           
|                                                
|                 /1\                            
|     zoo + I*asin|-| + zoo*x         otherwise  
\                 \x/
{−x2−x1−x2x2acosh⁡(1x)+1x1−x2x2for 1∣x2∣>1∞~x+iasin⁡(1x)+∞~otherwise\begin{cases} \frac{- x^{2} - x \sqrt{\frac{1 - x^{2}}{x^{2}}} \operatorname{acosh}{\left(\frac{1}{x} \right)} + 1}{x \sqrt{\frac{1 - x^{2}}{x^{2}}}} & \text{for}\: \frac{1}{\left|{x^{2}}\right|} > 1 \\\tilde{\infty} x + i \operatorname{asin}{\left(\frac{1}{x} \right)} + \tilde{\infty} & \text{otherwise} \end{cases} 
Piecewise(((1 - x^2 - x*sqrt((1 - x^2)/x^2)*acosh(1/x))/(x*sqrt((1 - x^2)/x^2)), 1/|x^2| > 1), (±oo + i*asin(1/x) + ±oo*x, True))
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