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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] 
  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |     ________   
 |  3 /  4        
 |  \/  x  - 2    
 |                
/                 
0
$$\int\limits_{0}^{1} \frac{1}{\sqrt[3]{x^{4} - 2}}\, dx$$ 
Integral(1/((x^4 - 2)^(1/3)), (x, 0, 1))
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                                  
      ------              _                  
 2/3    3                |_  /1/4, 1/3 |    \
2   *e      *Gamma(1/4)* |   |         | 1/2|
                        2  1 \  5/4    |    /
---------------------------------------------
                 8*Gamma(5/4)
$$\frac{2^{\frac{2}{3}} e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{3} \\ \frac{5}{4} \end{matrix}\middle| {\frac{1}{2}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)}$$ 
=
= 
      -pi*I                                  
      ------              _                  
 2/3    3                |_  /1/4, 1/3 |    \
2   *e      *Gamma(1/4)* |   |         | 1/2|
                        2  1 \  5/4    |    /
---------------------------------------------
                 8*Gamma(5/4)
$$\frac{2^{\frac{2}{3}} e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{3} \\ \frac{5}{4} \end{matrix}\middle| {\frac{1}{2}} \right)}}{8 \Gamma\left(\frac{5}{4}\right)}$$ 
2^(2/3)*exp(-pi*i/3)*gamma(1/4)*hyper((1/4, 1/3), (5/4,), 1/2)/(8*gamma(5/4))
Respuesta numérica [src] 
(0.413517378951148 - 0.716233110156101j)
(0.413517378951148 - 0.716233110156101j)

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

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