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Resolución de integrales/ x^5+1/ (x^5-1dx)/(x^5+1)^4

Integral de (x^5-1dx)/(x^5+1)^4 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1             
  /             
 |              
 |     5        
 |    x  - 1    
 |  --------- dx
 |          4   
 |  / 5    \    
 |  \x  + 1/    
 |              
/               
0
$$\int\limits_{0}^{1} \frac{x^{5} - 1}{\left(x^{5} + 1\right)^{4}}\, dx$$ 
Integral((x^5 - 1)/(x^5 + 1)^4, (x, 0, 1))
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
  349           /              4                3               2                                     /-625*t\\   78*log(2)          /              4                3               2                                     /    625*t\\
- ---- - RootSum|152587890625*t  - 19042968750*t  + 2376562500*t  - 296595000*t + 37015056, t -> t*log|------|| - --------- + RootSum|152587890625*t  - 19042968750*t  + 2376562500*t  - 296595000*t + 37015056, t -> t*log|1 - -----||
  3000          \                                                                                     \  78  //      625             \                                                                                     \      78 //
$$- \operatorname{RootSum} {\left(152587890625 t^{4} - 19042968750 t^{3} + 2376562500 t^{2} - 296595000 t + 37015056, \left( t \mapsto t \log{\left(- \frac{625 t}{78} \right)} \right)\right)} + \operatorname{RootSum} {\left(152587890625 t^{4} - 19042968750 t^{3} + 2376562500 t^{2} - 296595000 t + 37015056, \left( t \mapsto t \log{\left(1 - \frac{625 t}{78} \right)} \right)\right)} - \frac{349}{3000} - \frac{78 \log{\left(2 \right)}}{625}$$ 
=
= 
  349           /              4                3               2                                     /-625*t\\   78*log(2)          /              4                3               2                                     /    625*t\\
- ---- - RootSum|152587890625*t  - 19042968750*t  + 2376562500*t  - 296595000*t + 37015056, t -> t*log|------|| - --------- + RootSum|152587890625*t  - 19042968750*t  + 2376562500*t  - 296595000*t + 37015056, t -> t*log|1 - -----||
  3000          \                                                                                     \  78  //      625             \                                                                                     \      78 //
$$- \operatorname{RootSum} {\left(152587890625 t^{4} - 19042968750 t^{3} + 2376562500 t^{2} - 296595000 t + 37015056, \left( t \mapsto t \log{\left(- \frac{625 t}{78} \right)} \right)\right)} + \operatorname{RootSum} {\left(152587890625 t^{4} - 19042968750 t^{3} + 2376562500 t^{2} - 296595000 t + 37015056, \left( t \mapsto t \log{\left(1 - \frac{625 t}{78} \right)} \right)\right)} - \frac{349}{3000} - \frac{78 \log{\left(2 \right)}}{625}$$ 
-349/3000 - RootSum(152587890625*_t^4 - 19042968750*_t^3 + 2376562500*_t^2 - 296595000*_t + 37015056, Lambda(_t, _t*log(-625*_t/78))) - 78*log(2)/625 + RootSum(152587890625*_t^4 - 19042968750*_t^3 + 2376562500*_t^2 - 296595000*_t + 37015056, Lambda(_t, _t*log(1 - 625*_t/78)))
Respuesta numérica [src] 
-0.670641002668049
-0.670641002668049

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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