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Resolución de integrales/ (1/3)/ (x^4-2)/ 1/((x^4-2)^(1/3))

Integral de 1/((x^4-2)^(1/3)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2               
  /               
 |                
 |       1        
 |  ----------- dx
 |     ________   
 |  3 /  4        
 |  \/  x  - 2    
 |                
/                 
1
$$\int\limits_{1}^{2} \frac{1}{\sqrt[3]{x^{4} - 2}}\, dx$$ 
Integral(1/((x^4 - 2)^(1/3)), (x, 1, 2))
Respuesta (Indefinida) [src] 
                                -pi*I                                 
                                ------              _  /         |  4\
  /                        2/3    3                |_  |1/4, 1/3 | x |
 |                      x*2   *e      *Gamma(1/4)* |   |         | --|
 |      1                                         2  1 \  5/4    | 2 /
 | ----------- dx = C + ----------------------------------------------
 |    ________                           8*Gamma(5/4)                 
 | 3 /  4                                                             
 | \/  x  - 2                                                         
 |                                                                    
/
$$\int \frac{1}{\sqrt[3]{x^{4} - 2}}\, dx = C + \frac{2^{\frac{2}{3}} x e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{3} \\ \frac{5}{4} \end{matrix}\middle| {\frac{x^{4}}{2}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
        -pi*I                                           -pi*I                                
        ------              _                           ------              _                
   2/3    3                |_  /1/4, 1/3 |    \    2/3    3                |_  /1/4, 1/3 |  \
  2   *e      *Gamma(1/4)* |   |         | 1/2|   2   *e      *Gamma(1/4)* |   |         | 8|
                          2  1 \  5/4    |    /                           2  1 \  5/4    |  /
- --------------------------------------------- + -------------------------------------------
                   8*Gamma(5/4)                                   4*Gamma(5/4)
$$- \frac{2^{\frac{2}{3}} e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{3} \\ \frac{5}{4} \end{matrix}\middle| {\frac{1}{2}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)} + \frac{2^{\frac{2}{3}} e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{3} \\ \frac{5}{4} \end{matrix}\middle| {8} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$ 
=
= 
        -pi*I                                           -pi*I                                
        ------              _                           ------              _                
   2/3    3                |_  /1/4, 1/3 |    \    2/3    3                |_  /1/4, 1/3 |  \
  2   *e      *Gamma(1/4)* |   |         | 1/2|   2   *e      *Gamma(1/4)* |   |         | 8|
                          2  1 \  5/4    |    /                           2  1 \  5/4    |  /
- --------------------------------------------- + -------------------------------------------
                   8*Gamma(5/4)                                   4*Gamma(5/4)
$$- \frac{2^{\frac{2}{3}} e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{3} \\ \frac{5}{4} \end{matrix}\middle| {\frac{1}{2}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)} + \frac{2^{\frac{2}{3}} e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{3} \\ \frac{5}{4} \end{matrix}\middle| {8} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$ 
-2^(2/3)*exp(-pi*i/3)*gamma(1/4)*hyper((1/4, 1/3), (5/4,), 1/2)/(8*gamma(5/4)) + 2^(2/3)*exp(-pi*i/3)*gamma(1/4)*hyper((1/4, 1/3), (5/4,), 8)/(4*gamma(5/4))
Respuesta numérica [src] 
(0.734184458195492 - 0.236478721140744j)
(0.734184458195492 - 0.236478721140744j)

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

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