Descomposición de una fracción pi/(sqrt(1-x²)*(exp(x)-log(x)))+pi*(1/x-exp(x))*asin(x)/(exp(x)-log(x))² (número pi dividir por (raíz cuadrada de (1 menos x al cuadrado) multiplicar por (exponente de (x) menos logaritmo de (x))) más número pi multiplicar por (1 dividir por x menos exponente de (x)) multiplicar por ar coseno de eno de (x) dividir por (exponente de (x) menos logaritmo de (x)) al cuadrado)

Ha introducido [src]

                               /1    x\        
                            pi*|- - e |*asin(x)
            pi                 \x     /        
------------------------- + -------------------
   ________                                 2  
  /      2  / x         \      / x         \   
\/  1 - x  *\e  - log(x)/      \e  - log(x)/

\frac{\pi \left(- e^{x} + \frac{1}{x}\right) \operatorname{asin}{\left(x \right)}}{\left(e^{x} - \log{\left(x \right)}\right)^{2}} + \frac{\pi}{\sqrt{1 - x^{2}} \left(e^{x} - \log{\left(x \right)}\right)}

pi/((sqrt(1 - x^2)*(exp(x) - log(x)))) + ((pi*(1/x - exp(x)))*asin(x))/(exp(x) - log(x))^2

Simplificación general [src]

   /                      ________                    \
   |  /           x\     /      2  /        x\        |
pi*\x*\-log(x) + e / - \/  1 - x  *\-1 + x*e /*asin(x)/
-------------------------------------------------------
                  ________               2             
                 /      2  /           x\              
             x*\/  1 - x  *\-log(x) + e /

\frac{\pi \left(x \left(e^{x} - \log{\left(x \right)}\right) - \sqrt{1 - x^{2}} \left(x e^{x} - 1\right) \operatorname{asin}{\left(x \right)}\right)}{x \sqrt{1 - x^{2}} \left(e^{x} - \log{\left(x \right)}\right)^{2}}

pi*(x*(-log(x) + exp(x)) - sqrt(1 - x^2)*(-1 + x*exp(x))*asin(x))/(x*sqrt(1 - x^2)*(-log(x) + exp(x))^2)

Unión de expresiones racionales [src]

   /                      ________                   \
   |  /           x\     /      2  /       x\        |
pi*\x*\-log(x) + e / + \/  1 - x  *\1 - x*e /*asin(x)/
------------------------------------------------------
                 ________               2             
                /      2  /           x\              
            x*\/  1 - x  *\-log(x) + e /

\frac{\pi \left(x \left(e^{x} - \log{\left(x \right)}\right) + \sqrt{1 - x^{2}} \left(- x e^{x} + 1\right) \operatorname{asin}{\left(x \right)}\right)}{x \sqrt{1 - x^{2}} \left(e^{x} - \log{\left(x \right)}\right)^{2}}

pi*(x*(-log(x) + exp(x)) + sqrt(1 - x^2)*(1 - x*exp(x))*asin(x))/(x*sqrt(1 - x^2)*(-log(x) + exp(x))^2)

Denominador común [src]

 /                              ________                   ________           \ 
 |                    x        /      2                   /      2           x| 
-\pi*x*log(x) - pi*x*e  - pi*\/  1 - x  *asin(x) + pi*x*\/  1 - x  *asin(x)*e / 
--------------------------------------------------------------------------------
          ________                ________               ________               
         /      2     2          /      2   2*x         /      2   x            
     x*\/  1 - x  *log (x) + x*\/  1 - x  *e    - 2*x*\/  1 - x  *e *log(x)

- \frac{\pi x \sqrt{1 - x^{2}} e^{x} \operatorname{asin}{\left(x \right)} - \pi x e^{x} + \pi x \log{\left(x \right)} - \pi \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}}{x \sqrt{1 - x^{2}} e^{2 x} - 2 x \sqrt{1 - x^{2}} e^{x} \log{\left(x \right)} + x \sqrt{1 - x^{2}} \log{\left(x \right)}^{2}}

-(pi*x*log(x) - pi*x*exp(x) - pi*sqrt(1 - x^2)*asin(x) + pi*x*sqrt(1 - x^2)*asin(x)*exp(x))/(x*sqrt(1 - x^2)*log(x)^2 + x*sqrt(1 - x^2)*exp(2*x) - 2*x*sqrt(1 - x^2)*exp(x)*log(x))

Denominador racional [src]

                                                                                   ________               2                                                                                               
                                x                 2*x       2          x          /      2  /           x\        2                      3          2*x       3          x                        x       
pi*asin(x)*log(x) - pi*asin(x)*e  + pi*x*asin(x)*e    + pi*x *asin(x)*e  - pi*x*\/  1 - x  *\-log(x) + e /  - pi*x *asin(x)*log(x) - pi*x *asin(x)*e    + pi*x *asin(x)*e *log(x) - pi*x*asin(x)*e *log(x)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 3                                                                                        
                                                                                         /      2\ /           x\                                                                                         
                                                                                       x*\-1 + x /*\-log(x) + e /

\frac{- \pi x^{3} e^{2 x} \operatorname{asin}{\left(x \right)} + \pi x^{3} e^{x} \log{\left(x \right)} \operatorname{asin}{\left(x \right)} + \pi x^{2} e^{x} \operatorname{asin}{\left(x \right)} - \pi x^{2} \log{\left(x \right)} \operatorname{asin}{\left(x \right)} - \pi x \sqrt{1 - x^{2}} \left(e^{x} - \log{\left(x \right)}\right)^{2} + \pi x e^{2 x} \operatorname{asin}{\left(x \right)} - \pi x e^{x} \log{\left(x \right)} \operatorname{asin}{\left(x \right)} - \pi e^{x} \operatorname{asin}{\left(x \right)} + \pi \log{\left(x \right)} \operatorname{asin}{\left(x \right)}}{x \left(x^{2} - 1\right) \left(e^{x} - \log{\left(x \right)}\right)^{3}}

(pi*asin(x)*log(x) - pi*asin(x)*exp(x) + pi*x*asin(x)*exp(2*x) + pi*x^2*asin(x)*exp(x) - pi*x*sqrt(1 - x^2)*(-log(x) + exp(x))^2 - pi*x^2*asin(x)*log(x) - pi*x^3*asin(x)*exp(2*x) + pi*x^3*asin(x)*exp(x)*log(x) - pi*x*asin(x)*exp(x)*log(x))/(x*(-1 + x^2)*(-log(x) + exp(x))^3)

Combinatoria [src]

    /                     ________                ________           \ 
    |              x     /      2                /      2           x| 
-pi*\x*log(x) - x*e  - \/  1 - x  *asin(x) + x*\/  1 - x  *asin(x)*e / 
-----------------------------------------------------------------------
                                                      2                
                    ___________________ /           x\                 
                x*\/ -(1 + x)*(-1 + x) *\-log(x) + e /

- \frac{\pi \left(x \sqrt{1 - x^{2}} e^{x} \operatorname{asin}{\left(x \right)} - x e^{x} + x \log{\left(x \right)} - \sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}\right)}{x \sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(e^{x} - \log{\left(x \right)}\right)^{2}}

-pi*(x*log(x) - x*exp(x) - sqrt(1 - x^2)*asin(x) + x*sqrt(1 - x^2)*asin(x)*exp(x))/(x*sqrt(-(1 + x)*(-1 + x))*(-log(x) + exp(x))^2)

Respuesta numérica [src]

3.14159265358979*(1.0 - x^2)^(-0.5)/(-log(x) + exp(x)) + (3.14159265358979/x - 3.14159265358979*exp(x))*asin(x)/(-log(x) + exp(x))^2

3.14159265358979*(1.0 - x^2)^(-0.5)/(-log(x) + exp(x)) + (3.14159265358979/x - 3.14159265358979*exp(x))*asin(x)/(-log(x) + exp(x))^2

Parte trigonométrica [src]

                                               /  1                    \        
                                            pi*|- - + cosh(x) + sinh(x)|*asin(x)
                    pi                         \  x                    /        
----------------------------------------- - ------------------------------------
   ________                                                                 2   
  /      2                                     (-log(x) + cosh(x) + sinh(x))    
\/  1 - x  *(-log(x) + cosh(x) + sinh(x))

- \frac{\pi \left(\sinh{\left(x \right)} + \cosh{\left(x \right)} - \frac{1}{x}\right) \operatorname{asin}{\left(x \right)}}{\left(- \log{\left(x \right)} + \sinh{\left(x \right)} + \cosh{\left(x \right)}\right)^{2}} + \frac{\pi}{\sqrt{1 - x^{2}} \left(- \log{\left(x \right)} + \sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}

                                               /1                    \        
                                            pi*|- - cosh(x) - sinh(x)|*asin(x)
                    pi                         \x                    /        
----------------------------------------- + ----------------------------------
   ________                                                                2  
  /      2                                    (-log(x) + cosh(x) + sinh(x))   
\/  1 - x  *(-log(x) + cosh(x) + sinh(x))

\frac{\pi \left(- \sinh{\left(x \right)} - \cosh{\left(x \right)} + \frac{1}{x}\right) \operatorname{asin}{\left(x \right)}}{\left(- \log{\left(x \right)} + \sinh{\left(x \right)} + \cosh{\left(x \right)}\right)^{2}} + \frac{\pi}{\sqrt{1 - x^{2}} \left(- \log{\left(x \right)} + \sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}

pi/(sqrt(1 - x^2)*(-log(x) + cosh(x) + sinh(x))) + pi*(1/x - cosh(x) - sinh(x))*asin(x)/(-log(x) + cosh(x) + sinh(x))^2

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

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