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Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(x)*cos(x)+sin(x)/(2*sqrt(x))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
  ___           sin(x)
\/ x *cos(x) + -------
                   ___
               2*\/ x
xcos⁡(x)+sin⁡(x)2x\sqrt{x} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{2 \sqrt{x}} 
sqrt(x)*cos(x) + sin(x)/((2*sqrt(x)))
Simplificación general [src] 
sin(x)           
------ + x*cos(x)
  2              
-----------------
        ___      
      \/ x
xcos⁡(x)+sin⁡(x)2x\frac{x \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{2}}{\sqrt{x}} 
(sin(x)/2 + x*cos(x))/sqrt(x)
Respuesta numérica [src] 
x^0.5*cos(x) + 0.5*x^(-0.5)*sin(x)
x^0.5*cos(x) + 0.5*x^(-0.5)*sin(x)
Potencias [src] 
      / I*x    -I*x\     /   -I*x    I*x\
  ___ |e      e    |   I*\- e     + e   /
\/ x *|---- + -----| - ------------------
      \ 2       2  /            ___      
                            4*\/ x
x(eix2+e−ix2)−i(eix−e−ix)4x\sqrt{x} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) - \frac{i \left(e^{i x} - e^{- i x}\right)}{4 \sqrt{x}} 
sqrt(x)*(exp(i*x)/2 + exp(-i*x)/2) - i*(-exp(-i*x) + exp(i*x))/(4*sqrt(x))
Unión de expresiones racionales [src] 
2*x*cos(x) + sin(x)
-------------------
          ___      
      2*\/ x
2xcos⁡(x)+sin⁡(x)2x\frac{2 x \cos{\left(x \right)} + \sin{\left(x \right)}}{2 \sqrt{x}} 
(2*x*cos(x) + sin(x))/(2*sqrt(x))
Denominador común [src] 
2*x*cos(x) + sin(x)
-------------------
          ___      
      2*\/ x
2xcos⁡(x)+sin⁡(x)2x\frac{2 x \cos{\left(x \right)} + \sin{\left(x \right)}}{2 \sqrt{x}} 
(2*x*cos(x) + sin(x))/(2*sqrt(x))
Combinatoria [src] 
2*x*cos(x) + sin(x)
-------------------
          ___      
      2*\/ x
2xcos⁡(x)+sin⁡(x)2x\frac{2 x \cos{\left(x \right)} + \sin{\left(x \right)}}{2 \sqrt{x}} 
(2*x*cos(x) + sin(x))/(2*sqrt(x))
Denominador racional [src] 
  ___             3/2       
\/ x *sin(x) + 2*x   *cos(x)
----------------------------
            2*x
2x32cos⁡(x)+xsin⁡(x)2x\frac{2 x^{\frac{3}{2}} \cos{\left(x \right)} + \sqrt{x} \sin{\left(x \right)}}{2 x} 
(sqrt(x)*sin(x) + 2*x^(3/2)*cos(x))/(2*x)
Parte trigonométrica [src] 
  ___ /        2/x\\             /x\      
\/ x *|-1 + cot |-||          cot|-|      
      \         \2//             \2/      
-------------------- + -------------------
           2/x\          ___ /       2/x\\
    1 + cot |-|        \/ x *|1 + cot |-||
            \2/              \        \2//
x(cot⁡2(x2)−1)cot⁡2(x2)+1+cot⁡(x2)x(cot⁡2(x2)+1)\frac{\sqrt{x} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\cot{\left(\frac{x}{2} \right)}}{\sqrt{x} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
                  /    pi\
               cos|x - --|
  ___             \    2 /
\/ x *cos(x) + -----------
                     ___  
                 2*\/ x
xcos⁡(x)+cos⁡(x−π2)2x\sqrt{x} \cos{\left(x \right)} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{2 \sqrt{x}} 
  ___ /       2/x\\             /x\      
\/ x *|1 - tan |-||          tan|-|      
      \        \2//             \2/      
------------------- + -------------------
           2/x\         ___ /       2/x\\
    1 + tan |-|       \/ x *|1 + tan |-||
            \2/             \        \2//
x(1−tan⁡2(x2))tan⁡2(x2)+1+tan⁡(x2)x(tan⁡2(x2)+1)\frac{\sqrt{x} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{x} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
  ___                  
\/ x           1       
------ + --------------
sec(x)       ___       
         2*\/ x *csc(x)
xsec⁡(x)+12xcsc⁡(x)\frac{\sqrt{x}}{\sec{\left(x \right)}} + \frac{1}{2 \sqrt{x} \csc{\left(x \right)}} 
     ___                    
   \/ x             1       
----------- + --------------
   /pi    \       ___       
csc|-- - x|   2*\/ x *csc(x)
   \2     /
xcsc⁡(−x+π2)+12xcsc⁡(x)\frac{\sqrt{x}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{2 \sqrt{x} \csc{\left(x \right)}} 
  ___                       
\/ x              1         
------ + -------------------
sec(x)       ___    /    pi\
         2*\/ x *sec|x - --|
                    \    2 /
xsec⁡(x)+12xsec⁡(x−π2)\frac{\sqrt{x}}{\sec{\left(x \right)}} + \frac{1}{2 \sqrt{x} \sec{\left(x - \frac{\pi}{2} \right)}} 
  ___    /    pi\    sin(x)
\/ x *sin|x + --| + -------
         \    2 /       ___
                    2*\/ x
xsin⁡(x+π2)+sin⁡(x)2x\sqrt{x} \sin{\left(x + \frac{\pi}{2} \right)} + \frac{\sin{\left(x \right)}}{2 \sqrt{x}} 
sqrt(x)*sin(x + pi/2) + sin(x)/(2*sqrt(x))
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