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Resolución de integrales/ 3-x^2/ x^2-x/ x^3-x/ x/(x^3-x^2-x-1)

Integral de x/(x^3-x^2-x-1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |         x          
 |  --------------- dx
 |   3    2           
 |  x  - x  - x - 1   
 |                    
/                     
0
∫01x(−x+(x3−x2))−1 dx\int\limits_{0}^{1} \frac{x}{\left(- x + \left(x^{3} - x^{2}\right)\right) - 1}\, dx 
Integral(x/(x^3 - x^2 - x - 1), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                     
 |                                 /                           /              2       \\
 |        x                        |    3                      |1        220*t    22*t||
 | --------------- dx = C + RootSum|44*t  - 2*t - 1, t -> t*log|-- + x - ------ - ----||
 |  3    2                         \                           \17         17      17 //
 | x  - x  - x - 1                                                                      
 |                                                                                      
/
∫x(−x+(x3−x2))−1 dx=C+RootSum⁡(44t3−2t−1,(t↦tlog⁡(−220t217−22t17+x+117)))\int \frac{x}{\left(- x + \left(x^{3} - x^{2}\right)\right) - 1}\, dx = C + \operatorname{RootSum} {\left(44 t^{3} - 2 t - 1, \left( t \mapsto t \log{\left(- \frac{220 t^{2}}{17} - \frac{22 t}{17} + x + \frac{1}{17} \right)} \right)\right)}
Simplificar
Respuesta [src] 
         /                           /          2       \\          /                           /          2       \\
         |    3                      |1    220*t    22*t||          |    3                      |18   220*t    22*t||
- RootSum|44*t  - 2*t - 1, t -> t*log|-- - ------ - ----|| + RootSum|44*t  - 2*t - 1, t -> t*log|-- - ------ - ----||
         \                           \17     17      17 //          \                           \17     17      17 //
−RootSum⁡(44t3−2t−1,(t↦tlog⁡(−220t217−22t17+117)))+RootSum⁡(44t3−2t−1,(t↦tlog⁡(−220t217−22t17+1817)))- \operatorname{RootSum} {\left(44 t^{3} - 2 t - 1, \left( t \mapsto t \log{\left(- \frac{220 t^{2}}{17} - \frac{22 t}{17} + \frac{1}{17} \right)} \right)\right)} + \operatorname{RootSum} {\left(44 t^{3} - 2 t - 1, \left( t \mapsto t \log{\left(- \frac{220 t^{2}}{17} - \frac{22 t}{17} + \frac{18}{17} \right)} \right)\right)} 
=
= 
         /                           /          2       \\          /                           /          2       \\
         |    3                      |1    220*t    22*t||          |    3                      |18   220*t    22*t||
- RootSum|44*t  - 2*t - 1, t -> t*log|-- - ------ - ----|| + RootSum|44*t  - 2*t - 1, t -> t*log|-- - ------ - ----||
         \                           \17     17      17 //          \                           \17     17      17 //
−RootSum⁡(44t3−2t−1,(t↦tlog⁡(−220t217−22t17+117)))+RootSum⁡(44t3−2t−1,(t↦tlog⁡(−220t217−22t17+1817)))- \operatorname{RootSum} {\left(44 t^{3} - 2 t - 1, \left( t \mapsto t \log{\left(- \frac{220 t^{2}}{17} - \frac{22 t}{17} + \frac{1}{17} \right)} \right)\right)} + \operatorname{RootSum} {\left(44 t^{3} - 2 t - 1, \left( t \mapsto t \log{\left(- \frac{220 t^{2}}{17} - \frac{22 t}{17} + \frac{18}{17} \right)} \right)\right)} 
-RootSum(44*_t^3 - 2*_t - 1, Lambda(_t, _t*log(1/17 - 220*_t^2/17 - 22*_t/17))) + RootSum(44*_t^3 - 2*_t - 1, Lambda(_t, _t*log(18/17 - 220*_t^2/17 - 22*_t/17)))
Respuesta numérica [src] 
-0.289413986632603
-0.289413986632603

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

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