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Expresiones idénticas
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Simplificación de expresiones/ Descomposición en fracciones simples/ cos(x)*log(3-x)-sin(x)/(3-x)+x/((2+x^2)*sqrt(x^2+1))

¿Cómo vas a descomponer esta cos(x)log(3-x)-sin(x)/(3-x)+x/((2+x^2)sqrt(x^2+1)) expresión en fracciones?

Solución

Ha introducido [src]

                    sin(x)            x          
cos(x)*log(3 - x) - ------ + --------------------
                    3 - x                ________
                             /     2\   /  2     
                             \2 + x /*\/  x  + 1

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \left(\log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}\right)$$

cos(x)*log(3 - x) - sin(x)/(3 - x) + x/(((2 + x^2)*sqrt(x^2 + 1)))

Simplificación general [src]

sin(x)                                x          
------ + cos(x)*log(3 - x) + --------------------
-3 + x                          ________         
                               /      2  /     2\
                             \/  1 + x  *\2 + x /

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x - 3}$$

sin(x)/(-3 + x) + cos(x)*log(3 - x) + x/(sqrt(1 + x^2)*(2 + x^2))

Respuesta numérica [src]

cos(x)*log(3 - x) - sin(x)/(3.0 - x) + x*(1.0 + x^2)^(-0.5)/(2.0 + x^2)

cos(x)*log(3 - x) - sin(x)/(3.0 - x) + x*(1.0 + x^2)^(-0.5)/(2.0 + x^2)

Denominador común [src]

                       ________                ________                                  
        2             /      2            2   /      2                                   
       x  - 3*x + 2*\/  1 + x  *sin(x) + x *\/  1 + x  *sin(x)                           
--------------------------------------------------------------------- + cos(x)*log(3 - x)
       ________         ________           ________          ________                    
      /      2     3   /      2       2   /      2          /      2                     
- 6*\/  1 + x   + x *\/  1 + x   - 3*x *\/  1 + x   + 2*x*\/  1 + x

$$\log{\left(3 - x \right)} \cos{\left(x \right)} + \frac{x^{2} \sqrt{x^{2} + 1} \sin{\left(x \right)} + x^{2} - 3 x + 2 \sqrt{x^{2} + 1} \sin{\left(x \right)}}{x^{3} \sqrt{x^{2} + 1} - 3 x^{2} \sqrt{x^{2} + 1} + 2 x \sqrt{x^{2} + 1} - 6 \sqrt{x^{2} + 1}}$$

(x^2 - 3*x + 2*sqrt(1 + x^2)*sin(x) + x^2*sqrt(1 + x^2)*sin(x))/(-6*sqrt(1 + x^2) + x^3*sqrt(1 + x^2) - 3*x^2*sqrt(1 + x^2) + 2*x*sqrt(1 + x^2)) + cos(x)*log(3 - x)

Denominador racional [src]

                ________                ________               ________                           ________                             ________                            ________                  
 2             /      2            2   /      2               /      2                       3   /      2                         2   /      2                            /      2                   
x  - 3*x + 2*\/  1 + x  *sin(x) + x *\/  1 + x  *sin(x) - 6*\/  1 + x  *cos(x)*log(3 - x) + x *\/  1 + x  *cos(x)*log(3 - x) - 3*x *\/  1 + x  *cos(x)*log(3 - x) + 2*x*\/  1 + x  *cos(x)*log(3 - x)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                       ________                                                                                                      
                                                                                      /      2           /     2\                                                                                    
                                                                                    \/  1 + x  *(-3 + x)*\2 + x /

$$\frac{x^{3} \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} - 3 x^{2} \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} + x^{2} \sqrt{x^{2} + 1} \sin{\left(x \right)} + x^{2} + 2 x \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} - 3 x - 6 \sqrt{x^{2} + 1} \log{\left(3 - x \right)} \cos{\left(x \right)} + 2 \sqrt{x^{2} + 1} \sin{\left(x \right)}}{\left(x - 3\right) \sqrt{x^{2} + 1} \left(x^{2} + 2\right)}$$

(x^2 - 3*x + 2*sqrt(1 + x^2)*sin(x) + x^2*sqrt(1 + x^2)*sin(x) - 6*sqrt(1 + x^2)*cos(x)*log(3 - x) + x^3*sqrt(1 + x^2)*cos(x)*log(3 - x) - 3*x^2*sqrt(1 + x^2)*cos(x)*log(3 - x) + 2*x*sqrt(1 + x^2)*cos(x)*log(3 - x))/(sqrt(1 + x^2)*(-3 + x)*(2 + x^2))

Potencias [src]

/ I*x    -I*x\                                       /   -I*x    I*x\
|e      e    |                       x             I*\- e     + e   /
|---- + -----|*log(3 - x) + -------------------- + ------------------
\ 2       2  /                 ________                2*(3 - x)     
                              /      2  /     2\                     
                            \/  1 + x  *\2 + x /

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \log{\left(3 - x \right)} + \frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(3 - x\right)}$$

                    sin(x)            x          
cos(x)*log(3 - x) - ------ + --------------------
                    3 - x       ________         
                               /      2  /     2\
                             \/  1 + x  *\2 + x /

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$

cos(x)*log(3 - x) - sin(x)/(3 - x) + x/(sqrt(1 + x^2)*(2 + x^2))

Combinatoria [src]

                ________                ________               ________                           ________                             ________                            ________                  
 2             /      2            2   /      2               /      2                       3   /      2                         2   /      2                            /      2                   
x  - 3*x + 2*\/  1 + x  *sin(x) + x *\/  1 + x  *sin(x) - 6*\/  1 + x  *cos(x)*log(3 - x) + x *\/  1 + x  *cos(x)*log(3 - x) - 3*x *\/  1 + x  *cos(x)*log(3 - x) + 2*x*\/  1 + x  *cos(x)*log(3 - x)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                       ________                                                                                                      
                                                                                      /      2           /     2\                                                                                    
                                                                                    \/  1 + x  *(-3 + x)*\2 + x /

(x^2 - 3*x + 2*sqrt(1 + x^2)*sin(x) + x^2*sqrt(1 + x^2)*sin(x) - 6*sqrt(1 + x^2)*cos(x)*log(3 - x) + x^3*sqrt(1 + x^2)*cos(x)*log(3 - x) - 3*x^2*sqrt(1 + x^2)*cos(x)*log(3 - x) + 2*x*sqrt(1 + x^2)*cos(x)*log(3 - x))/(sqrt(1 + x^2)*(-3 + x)*(2 + x^2))

Compilar la expresión [src]

                    sin(x)            x          
cos(x)*log(3 - x) - ------ + --------------------
                    3 - x       ________         
                               /      2  /     2\
                             \/  1 + x  *\2 + x /

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$

cos(x)*log(3 - x) - sin(x)/(3 - x) + x/(sqrt(1 + x^2)*(2 + x^2))

Unión de expresiones racionales [src]

               ________                                               
              /      2  /     2\                                      
x*(3 - x) + \/  1 + x  *\2 + x /*(-sin(x) + (3 - x)*cos(x)*log(3 - x))
----------------------------------------------------------------------
                        ________                                      
                       /      2  /     2\                             
                     \/  1 + x  *\2 + x /*(3 - x)

$$\frac{x \left(3 - x\right) + \sqrt{x^{2} + 1} \left(x^{2} + 2\right) \left(\left(3 - x\right) \log{\left(3 - x \right)} \cos{\left(x \right)} - \sin{\left(x \right)}\right)}{\left(3 - x\right) \sqrt{x^{2} + 1} \left(x^{2} + 2\right)}$$

(x*(3 - x) + sqrt(1 + x^2)*(2 + x^2)*(-sin(x) + (3 - x)*cos(x)*log(3 - x)))/(sqrt(1 + x^2)*(2 + x^2)*(3 - x))

Abrimos la expresión [src]

                    sin(x)            x          
cos(x)*log(3 - x) - ------ + --------------------
                    3 - x                ________
                             /     2\   /  2     
                             \2 + x /*\/  x  + 1

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$

              x                                      sin(x)
------------------------------ + cos(x)*log(3 - x) - ------
     ________         ________                       3 - x 
    /  2         2   /  2                                  
2*\/  x  + 1  + x *\/  x  + 1

$$\frac{x}{x^{2} \sqrt{x^{2} + 1} + 2 \sqrt{x^{2} + 1}} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$

x/(2*sqrt(x^2 + 1) + x^2*sqrt(x^2 + 1)) + cos(x)*log(3 - x) - sin(x)/(3 - x)

Parte trigonométrica [src]

              /    pi\   sin(x)            x          
log(3 - x)*sin|x + --| - ------ + --------------------
              \    2 /   3 - x       ________         
                                    /      2  /     2\
                                  \/  1 + x  *\2 + x /

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \sin{\left(x + \frac{\pi}{2} \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$

log(3 - x)         1                   x          
---------- - -------------- + --------------------
  sec(x)     (3 - x)*csc(x)      ________         
                                /      2  /     2\
                              \/  1 + x  *\2 + x /

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \frac{\log{\left(3 - x \right)}}{\sec{\left(x \right)}} - \frac{1}{\left(3 - x\right) \csc{\left(x \right)}}$$

                       /        2/x\\                          /x\      
                       |-1 + cot |-||*log(3 - x)          2*cot|-|      
         x             \         \2//                          \2/      
-------------------- + ------------------------- - ---------------------
   ________                          2/x\          /       2/x\\        
  /      2  /     2\          1 + cot |-|          |1 + cot |-||*(3 - x)
\/  1 + x  *\2 + x /                  \2/          \        \2//

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \log{\left(3 - x \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \cot{\left(\frac{x}{2} \right)}}{\left(3 - x\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$

                       /       2/x\\                          /x\      
                       |1 - tan |-||*log(3 - x)          2*tan|-|      
         x             \        \2//                          \2/      
-------------------- + ------------------------ - ---------------------
   ________                         2/x\          /       2/x\\        
  /      2  /     2\         1 + tan |-|          |1 + tan |-||*(3 - x)
\/  1 + x  *\2 + x /                 \2/          \        \2//

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \log{\left(3 - x \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\left(3 - x\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$

         x                                 sin(x)
-------------------- + cos(x)*log(3 - x) - ------
            ________                       3 - x 
/     2\   /  2                                  
\2 + x /*\/  x  + 1

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$

                       /    pi\                       
                    cos|x - --|                       
                       \    2 /            x          
cos(x)*log(3 - x) - ----------- + --------------------
                       3 - x         ________         
                                    /      2  /     2\
                                  \/  1 + x  *\2 + x /

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{3 - x}$$

 log(3 - x)         1                   x          
----------- - -------------- + --------------------
   /pi    \   (3 - x)*csc(x)      ________         
csc|-- - x|                      /      2  /     2\
   \2     /                    \/  1 + x  *\2 + x /

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \frac{\log{\left(3 - x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{1}{\left(3 - x\right) \csc{\left(x \right)}}$$

                    sin(x)            x          
cos(x)*log(3 - x) - ------ + --------------------
                    3 - x       ________         
                               /      2  /     2\
                             \/  1 + x  *\2 + x /

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \log{\left(3 - x \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{3 - x}$$

log(3 - x)            1                     x          
---------- - ------------------- + --------------------
  sec(x)                /    pi\      ________         
             (3 - x)*sec|x - --|     /      2  /     2\
                        \    2 /   \/  1 + x  *\2 + x /

$$\frac{x}{\sqrt{x^{2} + 1} \left(x^{2} + 2\right)} + \frac{\log{\left(3 - x \right)}}{\sec{\left(x \right)}} - \frac{1}{\left(3 - x\right) \sec{\left(x - \frac{\pi}{2} \right)}}$$

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

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Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

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

Solución

¿Cómo vas a descomponer esta cos(x)log(3-x)-sin(x)/(3-x)+x/((2+x^2)sqrt(x^2+1)) expresión en fracciones?