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Integral de x^(-3)*(1+x^(-1))^(-1/5) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                  
  /                  
 |                   
 |        1          
 |  -------------- dx
 |         _______   
 |   3    /     1    
 |  x *5 /  1 + -    
 |     \/       x    
 |                   
/                    
0                    
$$\int\limits_{0}^{1} \frac{1}{x^{3} \sqrt[5]{1 + \frac{1}{x}}}\, dx$$
Integral(1/(x^3*(1 + 1/x)^(1/5)), (x, 0, 1))
Respuesta (Indefinida) [src]
  /                                                                                                                                                                                                                                                                                                                                                          
 |                                            9/5                                                             14/5                                                                  4/5                                                              4/5                                                      2        4/5                                   
 |       1                                 4*x   *Gamma(-9/5)*Gamma(14/5)                                  4*x    *Gamma(-9/5)*Gamma(14/5)                                 4*(1 + x)   *Gamma(1/5)*Gamma(9/5)                               x*(1 + x)   *Gamma(1/5)*Gamma(9/5)                             5*x *(1 + x)   *Gamma(1/5)*Gamma(9/5)             
 | -------------- dx = C - -------------------------------------------------------------- - -------------------------------------------------------------- - -------------------------------------------------------------- + -------------------------------------------------------------- + --------------------------------------------------------------
 |        _______             9/5                             14/5                             9/5                             14/5                             9/5                             14/5                             9/5                             14/5                             9/5                             14/5                       
 |  3    /     1           4*x   *Gamma(1/5)*Gamma(14/5) + 4*x    *Gamma(1/5)*Gamma(14/5)   4*x   *Gamma(1/5)*Gamma(14/5) + 4*x    *Gamma(1/5)*Gamma(14/5)   4*x   *Gamma(1/5)*Gamma(14/5) + 4*x    *Gamma(1/5)*Gamma(14/5)   4*x   *Gamma(1/5)*Gamma(14/5) + 4*x    *Gamma(1/5)*Gamma(14/5)   4*x   *Gamma(1/5)*Gamma(14/5) + 4*x    *Gamma(1/5)*Gamma(14/5)
 | x *5 /  1 + -                                                                                                                                                                                                                                                                                                                                             
 |    \/       x                                                                                                                                                                                                                                                                                                                                             
 |                                                                                                                                                                                                                                                                                                                                                           
/                                                                                                                                                                                                                                                                                                                                                            
$$\int \frac{1}{x^{3} \sqrt[5]{1 + \frac{1}{x}}}\, dx = C - \frac{4 x^{\frac{14}{5}} \Gamma\left(- \frac{9}{5}\right) \Gamma\left(\frac{14}{5}\right)}{4 x^{\frac{14}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right) + 4 x^{\frac{9}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right)} - \frac{4 x^{\frac{9}{5}} \Gamma\left(- \frac{9}{5}\right) \Gamma\left(\frac{14}{5}\right)}{4 x^{\frac{14}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right) + 4 x^{\frac{9}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right)} + \frac{5 x^{2} \left(x + 1\right)^{\frac{4}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{9}{5}\right)}{4 x^{\frac{14}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right) + 4 x^{\frac{9}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right)} + \frac{x \left(x + 1\right)^{\frac{4}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{9}{5}\right)}{4 x^{\frac{14}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right) + 4 x^{\frac{9}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right)} - \frac{4 \left(x + 1\right)^{\frac{4}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{9}{5}\right)}{4 x^{\frac{14}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right) + 4 x^{\frac{9}{5}} \Gamma\left(\frac{1}{5}\right) \Gamma\left(\frac{14}{5}\right)}$$
Respuesta numérica [src]
1.52774449873621e+34
1.52774449873621e+34

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