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Integral de (x-6)/(x^4+6x+8) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                
  /                
 |                 
 |     x - 6       
 |  ------------ dx
 |   4             
 |  x  + 6*x + 8   
 |                 
/                  
0                  
01x6(x4+6x)+8dx\int\limits_{0}^{1} \frac{x - 6}{\left(x^{4} + 6 x\right) + 8}\, dx
Integral((x - 6)/(x^4 + 6*x + 8), (x, 0, 1))
Solución detallada
  1. Vuelva a escribir el integrando:

    x6(x4+6x)+8=x(x4+6x)+86(x4+6x)+8\frac{x - 6}{\left(x^{4} + 6 x\right) + 8} = \frac{x}{\left(x^{4} + 6 x\right) + 8} - \frac{6}{\left(x^{4} + 6 x\right) + 8}

  2. Integramos término a término:

    1. No puedo encontrar los pasos en la búsqueda de esta integral.

      Pero la integral

      RootSum(24020t4+512t2+9t+2,(ttlog(8301312t369914919296t220973+776646t34955+x227152104865)))\operatorname{RootSum} {\left(24020 t^{4} + 512 t^{2} + 9 t + 2, \left( t \mapsto t \log{\left(\frac{8301312 t^{3}}{6991} - \frac{4919296 t^{2}}{20973} + \frac{776646 t}{34955} + x - \frac{227152}{104865} \right)} \right)\right)}

    1. La integral del producto de una función por una constante es la constante por la integral de esta función:

      (6(x4+6x)+8)dx=61(x4+6x)+8dx\int \left(- \frac{6}{\left(x^{4} + 6 x\right) + 8}\right)\, dx = - 6 \int \frac{1}{\left(x^{4} + 6 x\right) + 8}\, dx

      1. No puedo encontrar los pasos en la búsqueda de esta integral.

        Pero la integral

        RootSum(96080t4+648t2+48t+1,(ttlog(486405t36454045t2128+19127t256+x+729512)))\operatorname{RootSum} {\left(96080 t^{4} + 648 t^{2} + 48 t + 1, \left( t \mapsto t \log{\left(\frac{486405 t^{3}}{64} - \frac{54045 t^{2}}{128} + \frac{19127 t}{256} + x + \frac{729}{512} \right)} \right)\right)}

      Por lo tanto, el resultado es: 6RootSum(96080t4+648t2+48t+1,(ttlog(486405t36454045t2128+19127t256+x+729512)))- 6 \operatorname{RootSum} {\left(96080 t^{4} + 648 t^{2} + 48 t + 1, \left( t \mapsto t \log{\left(\frac{486405 t^{3}}{64} - \frac{54045 t^{2}}{128} + \frac{19127 t}{256} + x + \frac{729}{512} \right)} \right)\right)}

    El resultado es: 6RootSum(96080t4+648t2+48t+1,(ttlog(486405t36454045t2128+19127t256+x+729512)))+RootSum(24020t4+512t2+9t+2,(ttlog(8301312t369914919296t220973+776646t34955+x227152104865)))- 6 \operatorname{RootSum} {\left(96080 t^{4} + 648 t^{2} + 48 t + 1, \left( t \mapsto t \log{\left(\frac{486405 t^{3}}{64} - \frac{54045 t^{2}}{128} + \frac{19127 t}{256} + x + \frac{729}{512} \right)} \right)\right)} + \operatorname{RootSum} {\left(24020 t^{4} + 512 t^{2} + 9 t + 2, \left( t \mapsto t \log{\left(\frac{8301312 t^{3}}{6991} - \frac{4919296 t^{2}}{20973} + \frac{776646 t}{34955} + x - \frac{227152}{104865} \right)} \right)\right)}

  3. Ahora simplificar:

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\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{8301312 \left(- \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{3}}{6991} - \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} - \frac{4919296 \left(- \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{2}}{20973} - \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} \right)} + \left(\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{8301312 \left(\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{3}}{6991} - \frac{4919296 \left(\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{2}}{20973} + \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} - \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} \right)} + \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} + \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} + \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} - \frac{4919296 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} + \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{2}}{20973} + \frac{8301312 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} + \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{3}}{6991} \right)} + \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} - \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} - \frac{4919296 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} - \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{2}}{20973} - \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} + \frac{8301312 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} - \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{3}}{6991} \right)} - 6 \left(- \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right) \log{\left(x + \frac{729}{512} - \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} + \frac{486405 \left(- \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{3}}{64} - \frac{54045 \left(- \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{2}}{128} - \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} \right)} - 6 \left(\frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right) \log{\left(x + \frac{729}{512} + \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} - \frac{54045 \left(\frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{2}}{128} + \frac{486405 \left(\frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{3}}{64} - \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} \right)} - 6 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} + \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right) \log{\left(x + \frac{729}{512} + \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} + \frac{486405 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} + \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{3}}{64} - \frac{54045 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} + \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{2}}{128} + \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} \right)} - 6 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} - \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right) \log{\left(x + \frac{729}{512} + \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} - \frac{54045 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} - \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{2}}{128} + \frac{486405 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} - \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{3}}{64} - \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} \right)}

  4. Añadimos la constante de integración:

    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\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{8301312 \left(- \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{3}}{6991} - \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} - \frac{4919296 \left(- \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{2}}{20973} - \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} \right)} + \left(\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{8301312 \left(\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{3}}{6991} - \frac{4919296 \left(\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{2}}{20973} + \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} - \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} \right)} + \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} + \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} + \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} - \frac{4919296 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} + \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{2}}{20973} + \frac{8301312 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} + \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{3}}{6991} \right)} + \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} - \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} - \frac{4919296 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} - \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{2}}{20973} - \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} + \frac{8301312 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} - \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{3}}{6991} \right)} - 6 \left(- \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right) \log{\left(x + \frac{729}{512} - \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} + \frac{486405 \left(- \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{3}}{64} - \frac{54045 \left(- \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{2}}{128} - \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} \right)} - 6 \left(\frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right) \log{\left(x + \frac{729}{512} + \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} - \frac{54045 \left(\frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{2}}{128} + \frac{486405 \left(\frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{3}}{64} - \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} \right)} - 6 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} + \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right) \log{\left(x + \frac{729}{512} + \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} + \frac{486405 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} + \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{3}}{64} - \frac{54045 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} + \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{2}}{128} + \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} \right)} - 6 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} - \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right) \log{\left(x + \frac{729}{512} + \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} - \frac{54045 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} - \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{2}}{128} + \frac{486405 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} - \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{3}}{64} - \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} \right)}+ \mathrm{constant}


Respuesta:

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\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{8301312 \left(- \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{3}}{6991} - \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} - \frac{4919296 \left(- \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{2}}{20973} - \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} \right)} + \left(\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{8301312 \left(\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{3}}{6991} - \frac{4919296 \left(\frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2} - \frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2}\right)^{2}}{20973} + \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} - \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} \right)} + \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} + \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} + \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} - \frac{4919296 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} + \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{2}}{20973} + \frac{8301312 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} - \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} + \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{3}}{6991} \right)} + \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} - \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right) \log{\left(x - \frac{227152}{104865} + \frac{388323 \sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{34955} - \frac{4919296 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} - \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{2}}{20973} - \frac{388323 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{34955} + \frac{8301312 \left(\frac{\sqrt{- \frac{512}{18015} - 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}} + \frac{9}{12010 \sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}} - \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}}{2} - \frac{\sqrt{- \frac{256}{18015} + \frac{26207}{324540225 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}} + 2 \sqrt[3]{- \frac{362494841}{1496727591264000} + \frac{6991 \sqrt{18015} i}{11086871046400}}}}{2}\right)^{3}}{6991} \right)} - 6 \left(- \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right) \log{\left(x + \frac{729}{512} - \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} + \frac{486405 \left(- \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{3}}{64} - \frac{54045 \left(- \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{2}}{128} - \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} \right)} - 6 \left(\frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right) \log{\left(x + \frac{729}{512} + \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} - \frac{54045 \left(\frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{2}}{128} + \frac{486405 \left(\frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2} - \frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2}\right)^{3}}{64} - \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} \right)} - 6 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} + \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right) \log{\left(x + \frac{729}{512} + \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} + \frac{486405 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} + \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{3}}{64} - \frac{54045 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} - \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} + \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{2}}{128} + \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} \right)} - 6 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} - \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right) \log{\left(x + \frac{729}{512} + \frac{19127 \sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{512} - \frac{54045 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} - \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{2}}{128} + \frac{486405 \left(\frac{\sqrt{- \frac{54}{6005} - 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}} + \frac{6}{6005 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}} - \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}}{2} - \frac{\sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{2}\right)^{3}}{64} - \frac{19127 \sqrt{- \frac{27}{6005} + \frac{1024}{108180075 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}} + 2 \sqrt[3]{\frac{1152}{216540450125} + \frac{128 \sqrt{18015} i}{1948864051125}}}}{512} \right)}+ \mathrm{constant}

Respuesta (Indefinida) [src]
  /                                                                                                                                                                                                                         
 |                                /                                        /                 2                     3\\          /                                       /                        2                       3\\
 |    x - 6                       |       4        2                       |729       54045*t    19127*t   486405*t ||          |       4        2                      |  227152       4919296*t    776646*t   8301312*t ||
 | ------------ dx = C - 6*RootSum|96080*t  + 648*t  + 48*t + 1, t -> t*log|--- + x - -------- + ------- + ---------|| + RootSum|24020*t  + 512*t  + 9*t + 2, t -> t*log|- ------ + x - ---------- + -------- + ----------||
 |  4                             \                                        \512         128        256         64   //          \                                       \  104865         20973       34955        6991   //
 | x  + 6*x + 8                                                                                                                                                                                                             
 |                                                                                                                                                                                                                          
/                                                                                                                                                                                                                           
x6(x4+6x)+8dx=C+RootSum(24020t4+512t2+9t+2,(ttlog(8301312t369914919296t220973+776646t34955+x227152104865)))6RootSum(96080t4+648t2+48t+1,(ttlog(486405t36454045t2128+19127t256+x+729512)))\int \frac{x - 6}{\left(x^{4} + 6 x\right) + 8}\, dx = C + \operatorname{RootSum} {\left(24020 t^{4} + 512 t^{2} + 9 t + 2, \left( t \mapsto t \log{\left(\frac{8301312 t^{3}}{6991} - \frac{4919296 t^{2}}{20973} + \frac{776646 t}{34955} + x - \frac{227152}{104865} \right)} \right)\right)} - 6 \operatorname{RootSum} {\left(96080 t^{4} + 648 t^{2} + 48 t + 1, \left( t \mapsto t \log{\left(\frac{486405 t^{3}}{64} - \frac{54045 t^{2}}{128} + \frac{19127 t}{256} + x + \frac{729}{512} \right)} \right)\right)}
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902-2
Respuesta [src]
         /                                          /                      3                           2\\          /                                          /                      3                           2\\
         |      4         2                         |23465078   300499808*t    134508634*t   56764064*t ||          |      4         2                         |25116929   300499808*t    134508634*t   56764064*t ||
- RootSum|4804*t  + 1960*t  - 747*t + 67, t -> t*log|-------- - ------------ - ----------- - -----------|| + RootSum|4804*t  + 1960*t  - 747*t + 67, t -> t*log|-------- - ------------ - ----------- - -----------||
         \                                          \1651851      1651851        1651851       1651851  //          \                                          \1651851      1651851        1651851       1651851  //
RootSum(4804t4+1960t2747t+67,(ttlog(300499808t3165185156764064t21651851134508634t1651851+234650781651851)))+RootSum(4804t4+1960t2747t+67,(ttlog(300499808t3165185156764064t21651851134508634t1651851+251169291651851)))- \operatorname{RootSum} {\left(4804 t^{4} + 1960 t^{2} - 747 t + 67, \left( t \mapsto t \log{\left(- \frac{300499808 t^{3}}{1651851} - \frac{56764064 t^{2}}{1651851} - \frac{134508634 t}{1651851} + \frac{23465078}{1651851} \right)} \right)\right)} + \operatorname{RootSum} {\left(4804 t^{4} + 1960 t^{2} - 747 t + 67, \left( t \mapsto t \log{\left(- \frac{300499808 t^{3}}{1651851} - \frac{56764064 t^{2}}{1651851} - \frac{134508634 t}{1651851} + \frac{25116929}{1651851} \right)} \right)\right)}
=
=
         /                                          /                      3                           2\\          /                                          /                      3                           2\\
         |      4         2                         |23465078   300499808*t    134508634*t   56764064*t ||          |      4         2                         |25116929   300499808*t    134508634*t   56764064*t ||
- RootSum|4804*t  + 1960*t  - 747*t + 67, t -> t*log|-------- - ------------ - ----------- - -----------|| + RootSum|4804*t  + 1960*t  - 747*t + 67, t -> t*log|-------- - ------------ - ----------- - -----------||
         \                                          \1651851      1651851        1651851       1651851  //          \                                          \1651851      1651851        1651851       1651851  //
RootSum(4804t4+1960t2747t+67,(ttlog(300499808t3165185156764064t21651851134508634t1651851+234650781651851)))+RootSum(4804t4+1960t2747t+67,(ttlog(300499808t3165185156764064t21651851134508634t1651851+251169291651851)))- \operatorname{RootSum} {\left(4804 t^{4} + 1960 t^{2} - 747 t + 67, \left( t \mapsto t \log{\left(- \frac{300499808 t^{3}}{1651851} - \frac{56764064 t^{2}}{1651851} - \frac{134508634 t}{1651851} + \frac{23465078}{1651851} \right)} \right)\right)} + \operatorname{RootSum} {\left(4804 t^{4} + 1960 t^{2} - 747 t + 67, \left( t \mapsto t \log{\left(- \frac{300499808 t^{3}}{1651851} - \frac{56764064 t^{2}}{1651851} - \frac{134508634 t}{1651851} + \frac{25116929}{1651851} \right)} \right)\right)}
-RootSum(4804*_t^4 + 1960*_t^2 - 747*_t + 67, Lambda(_t, _t*log(23465078/1651851 - 300499808*_t^3/1651851 - 134508634*_t/1651851 - 56764064*_t^2/1651851))) + RootSum(4804*_t^4 + 1960*_t^2 - 747*_t + 67, Lambda(_t, _t*log(25116929/1651851 - 300499808*_t^3/1651851 - 134508634*_t/1651851 - 56764064*_t^2/1651851)))
Respuesta numérica [src]
-0.511307876283249
-0.511307876283249

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