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Resolución de integrales/ cos(4*x)/ x^2+c/ (x^2+cos(4*x))/(x^6+x+1)

Integral de (x^2+cos(4*x))/(x^6+x+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                 
  /                 
 |                  
 |   2              
 |  x  + cos(4*x)   
 |  ------------- dx
 |     6            
 |    x  + x + 1    
 |                  
/                   
2
∫2∞x2+cos⁡(4x)(x6+x)+1 dx\int\limits_{2}^{\infty} \frac{x^{2} + \cos{\left(4 x \right)}}{\left(x^{6} + x\right) + 1}\, dx 
Integral((x^2 + cos(4*x))/(x^6 + x + 1), (x, 2, oo))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                             
 |                          /                                                                                                                                                                                                   
 |  2                      |                        /                                                        /                                     4                   5                  3                  2                \\
 | x  + cos(4*x)           |  cos(4*x)              |       6         4        3        2                    |  120149527559       71586462219660*t    68806676598750*t    6403538301125*t    6348571040934*t    12262576500*t||
 | ------------- dx = C +  | ---------- dx + RootSum|43531*t  + 3888*t  - 100*t  + 108*t  - t + 1, t -> t*log|- ------------ + x - ----------------- - ----------------- - ---------------- - ---------------- - -------------||
 |    6                    |          6             \                                                        \  41852983441           41852983441         41852983441        41852983441        41852983441       41852983441 //
 |   x  + x + 1            | 1 + x + x                                                                                                                                                                                          
 |                         |                                                                                                                                                                                                    
/                         /
∫x2+cos⁡(4x)(x6+x)+1 dx=C+∫cos⁡(4x)x6+x+1 dx+RootSum⁡(43531t6+3888t4−100t3+108t2−t+1,(t↦tlog⁡(−68806676598750t541852983441−71586462219660t441852983441−6403538301125t341852983441−6348571040934t241852983441−12262576500t41852983441+x−12014952755941852983441)))\int \frac{x^{2} + \cos{\left(4 x \right)}}{\left(x^{6} + x\right) + 1}\, dx = C + \int \frac{\cos{\left(4 x \right)}}{x^{6} + x + 1}\, dx + \operatorname{RootSum} {\left(43531 t^{6} + 3888 t^{4} - 100 t^{3} + 108 t^{2} - t + 1, \left( t \mapsto t \log{\left(- \frac{68806676598750 t^{5}}{41852983441} - \frac{71586462219660 t^{4}}{41852983441} - \frac{6403538301125 t^{3}}{41852983441} - \frac{6348571040934 t^{2}}{41852983441} - \frac{12262576500 t}{41852983441} + x - \frac{120149527559}{41852983441} \right)} \right)\right)}
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    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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