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¿Cómo vas a descomponer esta atan(x^2/sqrt(-b^2/a^2))/(2*a^2*sqrt(-b^2/a^2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
    /      2     \
    |     x      |
atan|------------|
    |      ______|
    |     /   2  |
    |    /  -b   |
    |   /   ---- |
    |  /      2  |
    \\/      a   /
------------------
           ______ 
          /   2   
   2     /  -b    
2*a *   /   ----  
       /      2   
     \/      a    
$$\frac{\operatorname{atan}{\left(\frac{x^{2}}{\sqrt{\frac{\left(-1\right) b^{2}}{a^{2}}}} \right)}}{2 a^{2} \sqrt{\frac{\left(-1\right) b^{2}}{a^{2}}}}$$
atan(x^2/sqrt((-b^2)/a^2))/(((2*a^2)*sqrt((-b^2)/a^2)))
Simplificación general [src]
    /      2     \
    |     x      |
atan|------------|
    |      ______|
    |     /   2  |
    |    /  -b   |
    |   /   ---- |
    |  /      2  |
    \\/      a   /
------------------
           ______ 
          /   2   
   2     /  -b    
2*a *   /   ----  
       /      2   
     \/      a    
$$\frac{\operatorname{atan}{\left(\frac{x^{2}}{\sqrt{- \frac{b^{2}}{a^{2}}}} \right)}}{2 a^{2} \sqrt{- \frac{b^{2}}{a^{2}}}}$$
atan(x^2/sqrt(-b^2/a^2))/(2*a^2*sqrt(-b^2/a^2))
Respuesta numérica [src]
0.5*(-b^2/a^2)^(-0.5)*atan(x^2/sqrt((-b^2)/a^2))/a^2
0.5*(-b^2/a^2)^(-0.5)*atan(x^2/sqrt((-b^2)/a^2))/a^2
Unión de expresiones racionales [src]
    /      2     \
    |     x      |
atan|------------|
    |      ______|
    |     /   2  |
    |    /  -b   |
    |   /   ---- |
    |  /      2  |
    \\/      a   /
------------------
           ______ 
          /   2   
   2     /  -b    
2*a *   /   ----  
       /      2   
     \/      a    
$$\frac{\operatorname{atan}{\left(\frac{x^{2}}{\sqrt{- \frac{b^{2}}{a^{2}}}} \right)}}{2 a^{2} \sqrt{- \frac{b^{2}}{a^{2}}}}$$
atan(x^2/sqrt(-b^2/a^2))/(2*a^2*sqrt(-b^2/a^2))
Parte trigonométrica [src]
    /      2     \
    |     x      |
atan|------------|
    |      ______|
    |     /   2  |
    |    /  -b   |
    |   /   ---- |
    |  /      2  |
    \\/      a   /
------------------
           ______ 
          /   2   
   2     /  -b    
2*a *   /   ----  
       /      2   
     \/      a    
$$\frac{\operatorname{atan}{\left(\frac{x^{2}}{\sqrt{- \frac{b^{2}}{a^{2}}}} \right)}}{2 a^{2} \sqrt{- \frac{b^{2}}{a^{2}}}}$$
atan(x^2/sqrt(-b^2/a^2))/(2*a^2*sqrt(-b^2/a^2))
Denominador común [src]
    /      2     \
    |     x      |
atan|------------|
    |      ______|
    |     /   2  |
    |    /  -b   |
    |   /   ---- |
    |  /      2  |
    \\/      a   /
------------------
           ______ 
          /   2   
   2     /  -b    
2*a *   /   ----  
       /      2   
     \/      a    
$$\frac{\operatorname{atan}{\left(\frac{x^{2}}{\sqrt{- \frac{b^{2}}{a^{2}}}} \right)}}{2 a^{2} \sqrt{- \frac{b^{2}}{a^{2}}}}$$
atan(x^2/sqrt(-b^2/a^2))/(2*a^2*sqrt(-b^2/a^2))
Denominador racional [src]
                 /            ______\
                 |           /   2  |
                 | 2  2     /  -b   |
      ______     |a *x *   /   ---- |
     /   2       |        /      2  |
    /  -b        |      \/      a   |
   /   ---- *atan|------------------|
  /      2       |         2        |
\/      a        \        b         /
-------------------------------------
                    2                
                 2*b                 
$$\frac{\sqrt{- \frac{b^{2}}{a^{2}}} \operatorname{atan}{\left(\frac{a^{2} x^{2} \sqrt{- \frac{b^{2}}{a^{2}}}}{b^{2}} \right)}}{2 b^{2}}$$
sqrt(-b^2/a^2)*atan(a^2*x^2*sqrt(-b^2/a^2)/b^2)/(2*b^2)
Potencias [src]
    /      2     \
    |     x      |
atan|------------|
    |      ______|
    |     /   2  |
    |    /  -b   |
    |   /   ---- |
    |  /      2  |
    \\/      a   /
------------------
           ______ 
          /   2   
   2     /  -b    
2*a *   /   ----  
       /      2   
     \/      a    
$$\frac{\operatorname{atan}{\left(\frac{x^{2}}{\sqrt{- \frac{b^{2}}{a^{2}}}} \right)}}{2 a^{2} \sqrt{- \frac{b^{2}}{a^{2}}}}$$
atan(x^2/sqrt(-b^2/a^2))/(2*a^2*sqrt(-b^2/a^2))
Combinatoria [src]
    /      2     \
    |     x      |
atan|------------|
    |      ______|
    |     /   2  |
    |    /  -b   |
    |   /   ---- |
    |  /      2  |
    \\/      a   /
------------------
           ______ 
          /   2   
   2     /  -b    
2*a *   /   ----  
       /      2   
     \/      a    
$$\frac{\operatorname{atan}{\left(\frac{x^{2}}{\sqrt{- \frac{b^{2}}{a^{2}}}} \right)}}{2 a^{2} \sqrt{- \frac{b^{2}}{a^{2}}}}$$
atan(x^2/sqrt(-b^2/a^2))/(2*a^2*sqrt(-b^2/a^2))
Abrimos la expresión [src]
    /      2     \
    |     x      |
atan|------------|
    |      ______|
    |     /   2  |
    |    /  -b   |
    |   /   ---- |
    |  /      2  |
    \\/      a   /
------------------
           ______ 
          /   2   
   2     /  -b    
2*a *   /   ----  
       /      2   
     \/      a    
$$\frac{\operatorname{atan}{\left(\frac{x^{2}}{\sqrt{- \frac{b^{2}}{a^{2}}}} \right)}}{2 a^{2} \sqrt{- \frac{b^{2}}{a^{2}}}}$$
    /         2        \
    |        x         |
atan|------------------|
    |     ____    _____|
    |    / 1     /   2 |
    |   /  -- *\/  -b  |
    |  /    2          |
    \\/    a           /
------------------------
          ____    _____ 
   2     / 1     /   2  
2*a *   /  -- *\/  -b   
       /    2           
     \/    a            
$$\frac{\operatorname{atan}{\left(\frac{x^{2}}{\sqrt{- b^{2}} \sqrt{\frac{1}{a^{2}}}} \right)}}{2 a^{2} \sqrt{- b^{2}} \sqrt{\frac{1}{a^{2}}}}$$
atan(x^2/(sqrt(1/(a^2))*sqrt(-b^2)))/(2*a^2*sqrt(1/(a^2))*sqrt(-b^2))
Compilar la expresión [src]
    /      2     \
    |     x      |
atan|------------|
    |      ______|
    |     /   2  |
    |    /  -b   |
    |   /   ---- |
    |  /      2  |
    \\/      a   /
------------------
           ______ 
          /   2   
   2     /  -b    
2*a *   /   ----  
       /      2   
     \/      a    
$$\frac{\operatorname{atan}{\left(\frac{x^{2}}{\sqrt{\frac{\left(-1\right) b^{2}}{a^{2}}}} \right)}}{2 a^{2} \sqrt{- \frac{b^{2}}{a^{2}}}}$$
atan(x^2/sqrt((-b^2)/a^2))/(2*a^2*sqrt(-b^2/a^2))