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Integral de d{x}:
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Integral de x/(x^9+1/2)
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x dividir por (x en el grado nueve más uno dividir por dos)
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x/x9+1/2
x/(x⁹+1/2)
x/x^9+1/2
x dividir por (x^9+1 dividir por 2)
x/(x^9+1/2)dx
Expresiones semejantes
x/(x^9-1/2)

Integral de x/(x^9+1/2) dx

Solución

Ha introducido [src]

 oo          
  /          
 |           
 |    x      
 |  ------ dx
 |   9   1   
 |  x  + -   
 |       2   
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/            
1

$$\int\limits_{1}^{\infty} \frac{x}{x^{9} + \frac{1}{2}}\, dx$$

Integral(x/(x^9 + 1/2), (x, 1, oo))

Solución detallada

Vuelva a escribir el integrando:

$\frac{x}{x^{9} + \frac{1}{2}} = \frac{2 x}{2 x^{9} + 1}$
La integral del producto de una función por una constante es la constante por la integral de esta función:

$\int \frac{2 x}{2 x^{9} + 1}\, dx = 2 \int \frac{x}{2 x^{9} + 1}\, dx$
1. No puedo encontrar los pasos en la búsqueda de esta integral.
  
  Pero la integral
  
  $\operatorname{RootSum} {\left(1549681956 t^{9} + 1, \left( t \mapsto t \log{\left(- 118098 t^{5} + x \right)} \right)\right)}$
Por lo tanto, el resultado es: $2 \operatorname{RootSum} {\left(1549681956 t^{9} + 1, \left( t \mapsto t \log{\left(- 118098 t^{5} + x \right)} \right)\right)}$
Ahora simplificar:

$2 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{9}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{9}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(\frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(\frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18}\right)^{5} \right)}$
Añadimos la constante de integración:

$2 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{9}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{9}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(\frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(\frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18}\right)^{5} \right)}+ \mathrm{constant}$

Respuesta:

$2 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{9}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos^{2}{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin^{2}{\left(\frac{\pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{9}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)}}{36} + \frac{2^{\frac{7}{9}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{36} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)}}{36}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(\frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(\frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(- \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18}\right)^{5} \right)} + 2 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18}\right) \log{\left(x - 118098 \left(\frac{2^{\frac{7}{9}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)}}{18} - \frac{2^{\frac{7}{9}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}}{18} + \frac{2^{\frac{7}{9}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}}{18}\right)^{5} \right)}+ \mathrm{constant}$

Respuesta (Indefinida) [src]

  /                                                                       
 |                                                                        
 |   x                      /            9                /            5\\
 | ------ dx = C + 2*RootSum\1549681956*t  + 1, t -> t*log\x - 118098*t //
 |  9   1                                                                 
 | x  + -                                                                 
 |      2                                                                 
 |                                                                        
/

$$\int \frac{x}{x^{9} + \frac{1}{2}}\, dx = C + 2 \operatorname{RootSum} {\left(1549681956 t^{9} + 1, \left( t \mapsto t \log{\left(- 118098 t^{5} + x \right)} \right)\right)}$$

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