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Resolución de integrales/ x^4+4*x/ x^2+1/ 4*x+1/ (x^2+1)dx/(x^4+4*x+1)^2

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

Solución

Ha introducido [src]

  1                   
  /                   
 |                    
 |        2           
 |       x  + 1       
 |  --------------- dx
 |                2   
 |  / 4          \    
 |  \x  + 4*x + 1/    
 |                    
/                     
0

$$\int\limits_{0}^{1} \frac{x^{2} + 1}{\left(\left(x^{4} + 4 x\right) + 1\right)^{2}}\, dx$$

Integral((x^2 + 1)/(x^4 + 4*x + 1)^2, (x, 0, 1))

Solución detallada

Hay varias maneras de calcular esta integral.
Método #1
1. Vuelva a escribir el integrando:
  
  $\frac{x^{2} + 1}{\left(\left(x^{4} + 4 x\right) + 1\right)^{2}} = \frac{x^{2} + 1}{x^{8} + 8 x^{5} + 2 x^{4} + 16 x^{2} + 8 x + 1}$
2. Vuelva a escribir el integrando:
  
  $\frac{x^{2} + 1}{x^{8} + 8 x^{5} + 2 x^{4} + 16 x^{2} + 8 x + 1} = \frac{x^{2}}{x^{8} + 8 x^{5} + 2 x^{4} + 16 x^{2} + 8 x + 1} + \frac{1}{x^{8} + 8 x^{5} + 2 x^{4} + 16 x^{2} + 8 x + 1}$
3. Integramos término a término:
  1. No puedo encontrar los pasos en la búsqueda de esta integral.
    
    Pero la integral
    
    $\operatorname{RootSum} {\left(1151860736 t^{4} - 1213440 t^{2} - 11264 t - 433, \left( t \mapsto t \log{\left(- \frac{3172080484352 t^{3}}{63900493} + \frac{70126271488 t^{2}}{63900493} + \frac{4920673696 t}{63900493} + x - \frac{13672899}{63900493} \right)} \right)\right)} - \frac{x^{3} - 9 x^{2} + 3 x + 3}{104 x^{4} + 416 x + 104}$
  1. No puedo encontrar los pasos en la búsqueda de esta integral.
    
    Pero la integral
    
    $\operatorname{RootSum} {\left(1151860736 t^{4} - 764928 t^{2} - 13824 t - 81, \left( t \mapsto t \log{\left(- \frac{5255364608 t^{3}}{39393} + \frac{29246464 t^{2}}{4377} + \frac{3808 t}{4377} + x - \frac{1485}{1459} \right)} \right)\right)} - \frac{9 x^{3} - 3 x^{2} + x + 27}{104 x^{4} + 416 x + 104}$
  El resultado es: $\operatorname{RootSum} {\left(1151860736 t^{4} - 1213440 t^{2} - 11264 t - 433, \left( t \mapsto t \log{\left(- \frac{3172080484352 t^{3}}{63900493} + \frac{70126271488 t^{2}}{63900493} + \frac{4920673696 t}{63900493} + x - \frac{13672899}{63900493} \right)} \right)\right)} + \operatorname{RootSum} {\left(1151860736 t^{4} - 764928 t^{2} - 13824 t - 81, \left( t \mapsto t \log{\left(- \frac{5255364608 t^{3}}{39393} + \frac{29246464 t^{2}}{4377} + \frac{3808 t}{4377} + x - \frac{1485}{1459} \right)} \right)\right)} - \frac{x^{3} - 9 x^{2} + 3 x + 3}{104 x^{4} + 416 x + 104} - \frac{9 x^{3} - 3 x^{2} + x + 27}{104 x^{4} + 416 x + 104}$
Método #2
1. Vuelva a escribir el integrando:
  
  $\frac{x^{2} + 1}{\left(\left(x^{4} + 4 x\right) + 1\right)^{2}} = \frac{x^{2}}{x^{8} + 8 x^{5} + 2 x^{4} + 16 x^{2} + 8 x + 1} + \frac{1}{x^{8} + 8 x^{5} + 2 x^{4} + 16 x^{2} + 8 x + 1}$
2. Integramos término a término:
  1. No puedo encontrar los pasos en la búsqueda de esta integral.
    
    Pero la integral
    
    $\operatorname{RootSum} {\left(1151860736 t^{4} - 1213440 t^{2} - 11264 t - 433, \left( t \mapsto t \log{\left(- \frac{3172080484352 t^{3}}{63900493} + \frac{70126271488 t^{2}}{63900493} + \frac{4920673696 t}{63900493} + x - \frac{13672899}{63900493} \right)} \right)\right)} - \frac{x^{3} - 9 x^{2} + 3 x + 3}{104 x^{4} + 416 x + 104}$
  1. No puedo encontrar los pasos en la búsqueda de esta integral.
    
    Pero la integral
    
    $\operatorname{RootSum} {\left(1151860736 t^{4} - 764928 t^{2} - 13824 t - 81, \left( t \mapsto t \log{\left(- \frac{5255364608 t^{3}}{39393} + \frac{29246464 t^{2}}{4377} + \frac{3808 t}{4377} + x - \frac{1485}{1459} \right)} \right)\right)} - \frac{9 x^{3} - 3 x^{2} + x + 27}{104 x^{4} + 416 x + 104}$
  El resultado es: $\operatorname{RootSum} {\left(1151860736 t^{4} - 1213440 t^{2} - 11264 t - 433, \left( t \mapsto t \log{\left(- \frac{3172080484352 t^{3}}{63900493} + \frac{70126271488 t^{2}}{63900493} + \frac{4920673696 t}{63900493} + x - \frac{13672899}{63900493} \right)} \right)\right)} + \operatorname{RootSum} {\left(1151860736 t^{4} - 764928 t^{2} - 13824 t - 81, \left( t \mapsto t \log{\left(- \frac{5255364608 t^{3}}{39393} + \frac{29246464 t^{2}}{4377} + \frac{3808 t}{4377} + x - \frac{1485}{1459} \right)} \right)\right)} - \frac{x^{3} - 9 x^{2} + 3 x + 3}{104 x^{4} + 416 x + 104} - \frac{9 x^{3} - 3 x^{2} + x + 27}{104 x^{4} + 416 x + 104}$
Ahora simplificar:

$\frac{- 5 x^{3} + 6 x^{2} - 2 x + 52 \left(x^{4} + 4 x + 1\right) \left(\left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right) \log{\left(x - \frac{1485}{1459} - \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} + \frac{29246464 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{2}}{4377} - \frac{5255364608 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{3}}{39393} + \frac{1904 \sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{4377} \right)} + \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} - \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right) \log{\left(x - \frac{1485}{1459} - \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} - \frac{1904 \sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{4377} - \frac{5255364608 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} - \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{3}}{39393} + \frac{29246464 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} - \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{2}}{4377} \right)} + \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2} + \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2}\right) \log{\left(x - \frac{1485}{1459} - \frac{1904 \sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{4377} + \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} - \frac{5255364608 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2} + \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2}\right)^{3}}{39393} + \frac{29246464 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2} + \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2}\right)^{2}}{4377} \right)} + \left(\frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2}\right) \log{\left(x - \frac{3172080484352 \left(\frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2}\right)^{3}}{63900493} - \frac{13672899}{63900493} + \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} + \frac{70126271488 \left(\frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2}\right)^{2}}{63900493} + \frac{2460336848 \sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{63900493} \right)} + \left(\frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2}\right) \log{\left(x - \frac{5255364608 \left(\frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2}\right)^{3}}{39393} - \frac{1485}{1459} + \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} + \frac{1904 \sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{4377} + \frac{29246464 \left(\frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2}\right)^{2}}{4377} \right)} + \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right) \log{\left(x - \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} - \frac{13672899}{63900493} + \frac{70126271488 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{2}}{63900493} - \frac{3172080484352 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{3}}{63900493} + \frac{2460336848 \sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{63900493} \right)} + \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} - \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right) \log{\left(x - \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} - \frac{13672899}{63900493} - \frac{2460336848 \sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{63900493} - \frac{3172080484352 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} - \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{3}}{63900493} + \frac{70126271488 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} - \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{2}}{63900493} \right)} + \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2} + \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2}\right) \log{\left(x - \frac{2460336848 \sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{63900493} - \frac{13672899}{63900493} + \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} + \frac{70126271488 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2} + \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2}\right)^{2}}{63900493} - \frac{3172080484352 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2} + \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2}\right)^{3}}{63900493} \right)}\right) - 15}{52 \left(x^{4} + 4 x + 1\right)}$
Añadimos la constante de integración:

$\frac{- 5 x^{3} + 6 x^{2} - 2 x + 52 \left(x^{4} + 4 x + 1\right) \left(\left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right) \log{\left(x - \frac{1485}{1459} - \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} + \frac{29246464 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{2}}{4377} - \frac{5255364608 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{3}}{39393} + \frac{1904 \sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{4377} \right)} + \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} - \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right) \log{\left(x - \frac{1485}{1459} - \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} - \frac{1904 \sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{4377} - \frac{5255364608 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} - \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{3}}{39393} + \frac{29246464 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} - \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{2}}{4377} \right)} + \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2} + \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2}\right) \log{\left(x - \frac{1485}{1459} - \frac{1904 \sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{4377} + \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} - \frac{5255364608 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2} + \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2}\right)^{3}}{39393} + \frac{29246464 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2} + \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2}\right)^{2}}{4377} \right)} + \left(\frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2}\right) \log{\left(x - \frac{3172080484352 \left(\frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2}\right)^{3}}{63900493} - \frac{13672899}{63900493} + \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} + \frac{70126271488 \left(\frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2}\right)^{2}}{63900493} + \frac{2460336848 \sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{63900493} \right)} + \left(\frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2}\right) \log{\left(x - \frac{5255364608 \left(\frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2}\right)^{3}}{39393} - \frac{1485}{1459} + \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} + \frac{1904 \sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{4377} + \frac{29246464 \left(\frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2}\right)^{2}}{4377} \right)} + \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right) \log{\left(x - \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} - \frac{13672899}{63900493} + \frac{70126271488 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{2}}{63900493} - \frac{3172080484352 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{3}}{63900493} + \frac{2460336848 \sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{63900493} \right)} + \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} - \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right) \log{\left(x - \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} - \frac{13672899}{63900493} - \frac{2460336848 \sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{63900493} - \frac{3172080484352 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} - \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{3}}{63900493} + \frac{70126271488 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} - \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{2}}{63900493} \right)} + \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2} + \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2}\right) \log{\left(x - \frac{2460336848 \sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{63900493} - \frac{13672899}{63900493} + \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} + \frac{70126271488 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2} + \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2}\right)^{2}}{63900493} - \frac{3172080484352 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2} + \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2}\right)^{3}}{63900493} \right)}\right) - 15}{52 \left(x^{4} + 4 x + 1\right)}+ \mathrm{constant}$

Respuesta:

$\frac{- 5 x^{3} + 6 x^{2} - 2 x + 52 \left(x^{4} + 4 x + 1\right) \left(\left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right) \log{\left(x - \frac{1485}{1459} - \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} + \frac{29246464 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{2}}{4377} - \frac{5255364608 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{3}}{39393} + \frac{1904 \sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{4377} \right)} + \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} - \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right) \log{\left(x - \frac{1485}{1459} - \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} - \frac{1904 \sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{4377} - \frac{5255364608 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} - \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{3}}{39393} + \frac{29246464 \left(- \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} - \frac{\sqrt{- \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}} - 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216}}}{2}\right)^{2}}{4377} \right)} + \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2} + \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2}\right) \log{\left(x - \frac{1485}{1459} - \frac{1904 \sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{4377} + \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} - \frac{5255364608 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2} + \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2}\right)^{3}}{39393} + \frac{29246464 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2} + \frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2}\right)^{2}}{4377} \right)} + \left(\frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2}\right) \log{\left(x - \frac{3172080484352 \left(\frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2}\right)^{3}}{63900493} - \frac{13672899}{63900493} + \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} + \frac{70126271488 \left(\frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2}\right)^{2}}{63900493} + \frac{2460336848 \sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{63900493} \right)} + \left(\frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2}\right) \log{\left(x - \frac{5255364608 \left(\frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2}\right)^{3}}{39393} - \frac{1485}{1459} + \frac{1904 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{4377} + \frac{1904 \sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{4377} + \frac{29246464 \left(\frac{\sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + \frac{249}{281216} + \frac{27}{1124864 \sqrt{- \frac{56637}{2530638036992 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}}} + 2 \sqrt[3]{- \frac{1557603}{11386494499371876352} + \frac{118179 \sqrt{78}}{875884192259375104}} + \frac{249}{562432}}}}}{2}\right)^{2}}{4377} \right)} + \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right) \log{\left(x - \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} - \frac{13672899}{63900493} + \frac{70126271488 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{2}}{63900493} - \frac{3172080484352 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} + \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{3}}{63900493} + \frac{2460336848 \sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{63900493} \right)} + \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} - \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right) \log{\left(x - \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} - \frac{13672899}{63900493} - \frac{2460336848 \sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{63900493} - \frac{3172080484352 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} - \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{3}}{63900493} + \frac{70126271488 \left(- \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2} - \frac{\sqrt{- \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}} - 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216}}}{2}\right)^{2}}{63900493} \right)} + \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2} + \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2}\right) \log{\left(x - \frac{2460336848 \sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{63900493} - \frac{13672899}{63900493} + \frac{2460336848 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{63900493} + \frac{70126271488 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2} + \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2}\right)^{2}}{63900493} - \frac{3172080484352 \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + \frac{395}{281216} + \frac{11}{562432 \sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}}}{2} + \frac{\sqrt{- \frac{1434527}{7591914110976 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}}} + 2 \sqrt[3]{- \frac{745103393}{11386494499371876352} + \frac{63900493 \sqrt{78}}{7882957730334375936}} + \frac{395}{562432}}}{2}\right)^{3}}{63900493} \right)}\right) - 15}{52 \left(x^{4} + 4 x + 1\right)}+ \mathrm{constant}$

Respuesta (Indefinida) [src]

  /                                                                                                                                                                                                                                                                                                                            
 |                                                                                                                                                                                                                                                                                                                             
 |       2                       3      2                      2      3          /                                                      /                                3                               2\\          /                                                    /                         3                      2\\
 |      x  + 1              3 + x  - 9*x  + 3*x    27 + x - 3*x  + 9*x           |            4            2                            |  13672899       3172080484352*t    4920673696*t   70126271488*t ||          |            4           2                           |  1485       5255364608*t    3808*t   29246464*t ||
 | --------------- dx = C - -------------------- - -------------------- + RootSum|1151860736*t  - 1213440*t  - 11264*t - 433, t -> t*log|- -------- + x - ---------------- + ------------ + --------------|| + RootSum|1151860736*t  - 764928*t  - 13824*t - 81, t -> t*log|- ---- + x - ------------- + ------ + -----------||
 |               2                     4                      4                  \                                                      \  63900493           63900493         63900493        63900493   //          \                                                    \  1459           39393        4377        4377   //
 | / 4          \           104 + 104*x  + 416*x   104 + 104*x  + 416*x                                                                                                                                                                                                                                                        
 | \x  + 4*x + 1/                                                                                                                                                                                                                                                                                                              
 |                                                                                                                                                                                                                                                                                                                             
/

$$\int \frac{x^{2} + 1}{\left(\left(x^{4} + 4 x\right) + 1\right)^{2}}\, dx = C + \operatorname{RootSum} {\left(1151860736 t^{4} - 1213440 t^{2} - 11264 t - 433, \left( t \mapsto t \log{\left(- \frac{3172080484352 t^{3}}{63900493} + \frac{70126271488 t^{2}}{63900493} + \frac{4920673696 t}{63900493} + x - \frac{13672899}{63900493} \right)} \right)\right)} + \operatorname{RootSum} {\left(1151860736 t^{4} - 764928 t^{2} - 13824 t - 81, \left( t \mapsto t \log{\left(- \frac{5255364608 t^{3}}{39393} + \frac{29246464 t^{2}}{4377} + \frac{3808 t}{4377} + x - \frac{1485}{1459} \right)} \right)\right)} - \frac{x^{3} - 9 x^{2} + 3 x + 3}{104 x^{4} + 416 x + 104} - \frac{9 x^{3} - 3 x^{2} + x + 27}{104 x^{4} + 416 x + 104}$$

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Gráfica

Trazar el gráfico f(x)

Respuesta [src]

             /                                                     /                          3                               2\\          /                                                     /                          3                               2\\
 37          |           4            2                            |45053805   1370444308480*t    4987186784*t   28037235200*t ||          |           4            2                            |67542872   1370444308480*t    4987186784*t   28037235200*t ||
--- - RootSum|287965184*t  - 1082880*t  - 27392*t - 241, t -> t*log|-------- - ---------------- + ------------ + --------------|| + RootSum|287965184*t  - 1082880*t  - 27392*t - 241, t -> t*log|-------- - ---------------- + ------------ + --------------||
156          \                                                     \22489067       22489067         22489067        22489067   //          \                                                     \22489067       22489067         22489067        22489067   //

$$- \operatorname{RootSum} {\left(287965184 t^{4} - 1082880 t^{2} - 27392 t - 241, \left( t \mapsto t \log{\left(- \frac{1370444308480 t^{3}}{22489067} + \frac{28037235200 t^{2}}{22489067} + \frac{4987186784 t}{22489067} + \frac{45053805}{22489067} \right)} \right)\right)} + \operatorname{RootSum} {\left(287965184 t^{4} - 1082880 t^{2} - 27392 t - 241, \left( t \mapsto t \log{\left(- \frac{1370444308480 t^{3}}{22489067} + \frac{28037235200 t^{2}}{22489067} + \frac{4987186784 t}{22489067} + \frac{67542872}{22489067} \right)} \right)\right)} + \frac{37}{156}$$

             /                                                     /                          3                               2\\          /                                                     /                          3                               2\\
 37          |           4            2                            |45053805   1370444308480*t    4987186784*t   28037235200*t ||          |           4            2                            |67542872   1370444308480*t    4987186784*t   28037235200*t ||
--- - RootSum|287965184*t  - 1082880*t  - 27392*t - 241, t -> t*log|-------- - ---------------- + ------------ + --------------|| + RootSum|287965184*t  - 1082880*t  - 27392*t - 241, t -> t*log|-------- - ---------------- + ------------ + --------------||
156          \                                                     \22489067       22489067         22489067        22489067   //          \                                                     \22489067       22489067         22489067        22489067   //

37/156 - RootSum(287965184*_t^4 - 1082880*_t^2 - 27392*_t - 241, Lambda(_t, _t*log(45053805/22489067 - 1370444308480*_t^3/22489067 + 4987186784*_t/22489067 + 28037235200*_t^2/22489067))) + RootSum(287965184*_t^4 - 1082880*_t^2 - 27392*_t - 241, Lambda(_t, _t*log(67542872/22489067 - 1370444308480*_t^3/22489067 + 4987186784*_t/22489067 + 28037235200*_t^2/22489067)))

Respuesta numérica [src]

0.216777577577753

0.216777577577753

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

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Método #2