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Simplificación de expresiones/ Descomposición en fracciones simples/ acot(x^3)^2/(x+13/10)-6*x^2*acot(x^3)*log(x+13/10)/(1+x^6)

¿Cómo vas a descomponer esta acot(x^3)^2/(x+13/10)-6*x^2*acot(x^3)*log(x+13/10)/(1+x^6) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
               2     / 3\    /    13\
    2/ 3\   6*x *acot\x /*log|x + --|
acot \x /                    \    10/
--------- - -------------------------
      13                   6         
  x + --              1 + x          
      10
−6x2acot⁡(x3)log⁡(x+1310)x6+1+acot⁡2(x3)x+1310- \frac{6 x^{2} \operatorname{acot}{\left(x^{3} \right)} \log{\left(x + \frac{13}{10} \right)}}{x^{6} + 1} + \frac{\operatorname{acot}^{2}{\left(x^{3} \right)}}{x + \frac{13}{10}} 
acot(x^3)^2/(x + 13/10) - ((6*x^2)*acot(x^3))*log(x + 13/10)/(1 + x^6)
Simplificación general [src] 
  /  /     6\     / 3\      2                /13    \\     / 3\
2*|5*\1 + x /*acot\x / - 3*x *(13 + 10*x)*log|-- + x||*acot\x /
  \                                          \10    //         
---------------------------------------------------------------
                      /     6\                                 
                      \1 + x /*(13 + 10*x)
2(−3x2(10x+13)log⁡(x+1310)+5(x6+1)acot⁡(x3))acot⁡(x3)(10x+13)(x6+1)\frac{2 \left(- 3 x^{2} \left(10 x + 13\right) \log{\left(x + \frac{13}{10} \right)} + 5 \left(x^{6} + 1\right) \operatorname{acot}{\left(x^{3} \right)}\right) \operatorname{acot}{\left(x^{3} \right)}}{\left(10 x + 13\right) \left(x^{6} + 1\right)} 
2*(5*(1 + x^6)*acot(x^3) - 3*x^2*(13 + 10*x)*log(13/10 + x))*acot(x^3)/((1 + x^6)*(13 + 10*x))
Respuesta numérica [src] 
acot(x^3)^2/(1.3 + x) - 6.0*x^2*acot(x^3)*log(x + 13/10)/(1.0 + x^6)
acot(x^3)^2/(1.3 + x) - 6.0*x^2*acot(x^3)*log(x + 13/10)/(1.0 + x^6)
Denominador racional [src] 
       2/ 3\       6     2/ 3\       2     / 3\    /13    \       3     / 3\    /13    \
10*acot \x / + 10*x *acot \x / - 78*x *acot\x /*log|-- + x| - 60*x *acot\x /*log|-- + x|
                                                   \10    /                     \10    /
----------------------------------------------------------------------------------------
                                  /     6\                                              
                                  \1 + x /*(13 + 10*x)
10x6acot⁡2(x3)−60x3log⁡(x+1310)acot⁡(x3)−78x2log⁡(x+1310)acot⁡(x3)+10acot⁡2(x3)(10x+13)(x6+1)\frac{10 x^{6} \operatorname{acot}^{2}{\left(x^{3} \right)} - 60 x^{3} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)} - 78 x^{2} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)} + 10 \operatorname{acot}^{2}{\left(x^{3} \right)}}{\left(10 x + 13\right) \left(x^{6} + 1\right)} 
(10*acot(x^3)^2 + 10*x^6*acot(x^3)^2 - 78*x^2*acot(x^3)*log(13/10 + x) - 60*x^3*acot(x^3)*log(13/10 + x))/((1 + x^6)*(13 + 10*x))
Unión de expresiones racionales [src] 
  /  /     6\     / 3\      2                /13 + 10*x\\     / 3\
2*|5*\1 + x /*acot\x / - 3*x *(13 + 10*x)*log|---------||*acot\x /
  \                                          \    10   //         
------------------------------------------------------------------
                       /     6\                                   
                       \1 + x /*(13 + 10*x)
2(−3x2(10x+13)log⁡(10x+1310)+5(x6+1)acot⁡(x3))acot⁡(x3)(10x+13)(x6+1)\frac{2 \left(- 3 x^{2} \left(10 x + 13\right) \log{\left(\frac{10 x + 13}{10} \right)} + 5 \left(x^{6} + 1\right) \operatorname{acot}{\left(x^{3} \right)}\right) \operatorname{acot}{\left(x^{3} \right)}}{\left(10 x + 13\right) \left(x^{6} + 1\right)} 
2*(5*(1 + x^6)*acot(x^3) - 3*x^2*(13 + 10*x)*log((13 + 10*x)/10))*acot(x^3)/((1 + x^6)*(13 + 10*x))
Potencias [src] 
               2     / 3\    /13    \
    2/ 3\   6*x *acot\x /*log|-- + x|
acot \x /                    \10    /
--------- - -------------------------
  13                       6         
  -- + x              1 + x          
  10
−6x2log⁡(x+1310)acot⁡(x3)x6+1+acot⁡2(x3)x+1310- \frac{6 x^{2} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)}}{x^{6} + 1} + \frac{\operatorname{acot}^{2}{\left(x^{3} \right)}}{x + \frac{13}{10}} 
acot(x^3)^2/(13/10 + x) - 6*x^2*acot(x^3)*log(13/10 + x)/(1 + x^6)
Parte trigonométrica [src] 
               2     / 3\    /13    \
    2/ 3\   6*x *acot\x /*log|-- + x|
acot \x /                    \10    /
--------- - -------------------------
  13                       6         
  -- + x              1 + x          
  10
−6x2log⁡(x+1310)acot⁡(x3)x6+1+acot⁡2(x3)x+1310- \frac{6 x^{2} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)}}{x^{6} + 1} + \frac{\operatorname{acot}^{2}{\left(x^{3} \right)}}{x + \frac{13}{10}} 
acot(x^3)^2/(13/10 + x) - 6*x^2*acot(x^3)*log(13/10 + x)/(1 + x^6)
Denominador común [src] 
       2/ 3\       6     2/ 3\       2     / 3\    /13    \       3     / 3\    /13    \
10*acot \x / + 10*x *acot \x / - 78*x *acot\x /*log|-- + x| - 60*x *acot\x /*log|-- + x|
                                                   \10    /                     \10    /
----------------------------------------------------------------------------------------
                                               7       6                                
                               13 + 10*x + 10*x  + 13*x
10x6acot⁡2(x3)−60x3log⁡(x+1310)acot⁡(x3)−78x2log⁡(x+1310)acot⁡(x3)+10acot⁡2(x3)10x7+13x6+10x+13\frac{10 x^{6} \operatorname{acot}^{2}{\left(x^{3} \right)} - 60 x^{3} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)} - 78 x^{2} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)} + 10 \operatorname{acot}^{2}{\left(x^{3} \right)}}{10 x^{7} + 13 x^{6} + 10 x + 13} 
(10*acot(x^3)^2 + 10*x^6*acot(x^3)^2 - 78*x^2*acot(x^3)*log(13/10 + x) - 60*x^3*acot(x^3)*log(13/10 + x))/(13 + 10*x + 10*x^7 + 13*x^6)
Combinatoria [src] 
  /      / 3\       2    /13    \       3    /13    \      6     / 3\\     / 3\
2*|5*acot\x / - 39*x *log|-- + x| - 30*x *log|-- + x| + 5*x *acot\x /|*acot\x /
  \                      \10    /            \10    /                /         
-------------------------------------------------------------------------------
                       /     2\             /     4    2\                      
                       \1 + x /*(13 + 10*x)*\1 + x  - x /
2(5x6acot⁡(x3)−30x3log⁡(x+1310)−39x2log⁡(x+1310)+5acot⁡(x3))acot⁡(x3)(10x+13)(x2+1)(x4−x2+1)\frac{2 \left(5 x^{6} \operatorname{acot}{\left(x^{3} \right)} - 30 x^{3} \log{\left(x + \frac{13}{10} \right)} - 39 x^{2} \log{\left(x + \frac{13}{10} \right)} + 5 \operatorname{acot}{\left(x^{3} \right)}\right) \operatorname{acot}{\left(x^{3} \right)}}{\left(10 x + 13\right) \left(x^{2} + 1\right) \left(x^{4} - x^{2} + 1\right)} 
2*(5*acot(x^3) - 39*x^2*log(13/10 + x) - 30*x^3*log(13/10 + x) + 5*x^6*acot(x^3))*acot(x^3)/((1 + x^2)*(13 + 10*x)*(1 + x^4 - x^2))
Compilar la expresión [src] 
               2     / 3\    /    13\
    2/ 3\   6*x *acot\x /*log|x + --|
acot \x /                    \    10/
--------- - -------------------------
  13                       6         
  -- + x              1 + x          
  10
−6x2log⁡(x+1310)acot⁡(x3)x6+1+acot⁡2(x3)x+1310- \frac{6 x^{2} \log{\left(x + \frac{13}{10} \right)} \operatorname{acot}{\left(x^{3} \right)}}{x^{6} + 1} + \frac{\operatorname{acot}^{2}{\left(x^{3} \right)}}{x + \frac{13}{10}} 
acot(x^3)^2/(13/10 + x) - 6*x^2*acot(x^3)*log(x + 13/10)/(1 + x^6)
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