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Resolución de integrales/ (7x^2+x-(arctg(8x)^2))/(2x^7-x^3+4)

Integral de (7x^2+x-(arctg(8x)^2))/(2x^7-x^3+4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                         
  /                         
 |                          
 |     2           2        
 |  7*x  + x - atan (8*x)   
 |  --------------------- dx
 |         7    3           
 |      2*x  - x  + 4       
 |                          
/                           
1
∫1∞(7x2+x)−atan⁡2(8x)(2x7−x3)+4 dx\int\limits_{1}^{\infty} \frac{\left(7 x^{2} + x\right) - \operatorname{atan}^{2}{\left(8 x \right)}}{\left(2 x^{7} - x^{3}\right) + 4}\, dx 
Integral((7*x^2 + x - atan(8*x)^2)/(2*x^7 - x^3 + 4), (x, 1, oo))
Respuesta (Indefinida) [src] 
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 |                                 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
 |    2           2                |       2                     /                                                                       /              2              3        4              5               6\\          /                                                             /                                                                             3                             2                              6                               5                                4\\
 | 7*x  + x - atan (8*x)           |   atan (8*x)                |            7         5        4        3       2                      | 51       95*t    11*t   24*t    216*t    210826144*t    1264956864*t ||          |            7            5        4         3                | 35017530913884562344       6670024174736842976*t   38892520282129683769440*t    144135058974998369220236*t    8931606587684877249221120*t    46634544318935136053174272*t    175786210992577898590665984*t ||
 | --------------------- dx = C -  | ------------- dx + 7*RootSum|1686609152*t  + 2016*t  - 112*t  - 203*t  + 21*t  + 7*t - 1, t -> t*log|--- + x - ----- - ---- + ----- + ------ + ------------ + -------------|| + RootSum|3373218304*t  + 4302592*t  - 128*t  + 2156*t  + 1, t -> t*log|--------------------- + x + --------------------- + -------------------------- + --------------------------- + ---------------------------- + ----------------------------- + ------------------------------||
 |        7    3                   |      3      7               \                                                                       \392         28     56      7       7           49              49     //          \                                                             \571960101912267146293       571960101912267146293     571960101912267146293         571960101912267146293         571960101912267146293           571960101912267146293           571960101912267146293     //
 |     2*x  - x  + 4               | 4 - x  + 2*x                                                                                                                                                                                                                                                                                                                                                                                                                                                        
 |                                 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
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∫(7x2+x)−atan⁡2(8x)(2x7−x3)+4 dx=C−∫atan⁡2(8x)2x7−x3+4 dx+RootSum⁡(3373218304t7+4302592t5−128t4+2156t3+1,(t↦tlog⁡(8931606587684877249221120t6571960101912267146293+46634544318935136053174272t5571960101912267146293+175786210992577898590665984t4571960101912267146293+38892520282129683769440t3571960101912267146293+144135058974998369220236t2571960101912267146293+6670024174736842976t571960101912267146293+x+35017530913884562344571960101912267146293)))+7RootSum⁡(1686609152t7+2016t5−112t4−203t3+21t2+7t−1,(t↦tlog⁡(1264956864t649+210826144t549+216t47+24t37−95t228−11t56+x+51392)))\int \frac{\left(7 x^{2} + x\right) - \operatorname{atan}^{2}{\left(8 x \right)}}{\left(2 x^{7} - x^{3}\right) + 4}\, dx = C - \int \frac{\operatorname{atan}^{2}{\left(8 x \right)}}{2 x^{7} - x^{3} + 4}\, dx + \operatorname{RootSum} {\left(3373218304 t^{7} + 4302592 t^{5} - 128 t^{4} + 2156 t^{3} + 1, \left( t \mapsto t \log{\left(\frac{8931606587684877249221120 t^{6}}{571960101912267146293} + \frac{46634544318935136053174272 t^{5}}{571960101912267146293} + \frac{175786210992577898590665984 t^{4}}{571960101912267146293} + \frac{38892520282129683769440 t^{3}}{571960101912267146293} + \frac{144135058974998369220236 t^{2}}{571960101912267146293} + \frac{6670024174736842976 t}{571960101912267146293} + x + \frac{35017530913884562344}{571960101912267146293} \right)} \right)\right)} + 7 \operatorname{RootSum} {\left(1686609152 t^{7} + 2016 t^{5} - 112 t^{4} - 203 t^{3} + 21 t^{2} + 7 t - 1, \left( t \mapsto t \log{\left(\frac{1264956864 t^{6}}{49} + \frac{210826144 t^{5}}{49} + \frac{216 t^{4}}{7} + \frac{24 t^{3}}{7} - \frac{95 t^{2}}{28} - \frac{11 t}{56} + x + \frac{51}{392} \right)} \right)\right)}
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