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Resolución de integrales/ x/(x^6-1)/ (1/3)/ x/(x^6-1)^(1/3)

Integral de x/(x^6-1)^(1/3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 6/5              
  /               
 |                
 |       x        
 |  ----------- dx
 |     ________   
 |  3 /  6        
 |  \/  x  - 1    
 |                
/                 
1
$$\int\limits_{1}^{\frac{6}{5}} \frac{x}{\sqrt[3]{x^{6} - 1}}\, dx$$ 
Integral(x/(x^6 - 1)^(1/3), (x, 1, 6/5))
Respuesta (Indefinida) [src] 
                            -pi*I                                 
                            ------              _                 
  /                      2    3                |_  /1/3, 1/3 |  6\
 |                      x *e      *Gamma(1/3)* |   |         | x |
 |      x                                     2  1 \  4/3    |   /
 | ----------- dx = C + ------------------------------------------
 |    ________                         6*Gamma(4/3)               
 | 3 /  6                                                         
 | \/  x  - 1                                                     
 |                                                                
/
$$\int \frac{x}{\sqrt[3]{x^{6} - 1}}\, dx = C + \frac{x^{2} e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {x^{6}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
   -pi*I                                      -pi*I                                    
   ------              _                      ------              _                    
     3                |_  /1/3, 1/3 |  \        3                |_  /1/3, 1/3 | 46656\
  e      *Gamma(1/3)* |   |         | 1|   6*e      *Gamma(1/3)* |   |         | -----|
                     2  1 \  4/3    |  /                        2  1 \  4/3    | 15625/
- -------------------------------------- + --------------------------------------------
               6*Gamma(4/3)                               25*Gamma(4/3)
$$- \frac{e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {1} \right)}}{6 \Gamma\left(\frac{4}{3}\right)} + \frac{6 e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{46656}{15625}} \right)}}{25 \Gamma\left(\frac{4}{3}\right)}$$ 
=
= 
   -pi*I                                      -pi*I                                    
   ------              _                      ------              _                    
     3                |_  /1/3, 1/3 |  \        3                |_  /1/3, 1/3 | 46656\
  e      *Gamma(1/3)* |   |         | 1|   6*e      *Gamma(1/3)* |   |         | -----|
                     2  1 \  4/3    |  /                        2  1 \  4/3    | 15625/
- -------------------------------------- + --------------------------------------------
               6*Gamma(4/3)                               25*Gamma(4/3)
$$- \frac{e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {1} \right)}}{6 \Gamma\left(\frac{4}{3}\right)} + \frac{6 e^{- \frac{i \pi}{3}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{46656}{15625}} \right)}}{25 \Gamma\left(\frac{4}{3}\right)}$$ 
-exp(-pi*i/3)*gamma(1/3)*hyper((1/3, 1/3), (4/3,), 1)/(6*gamma(4/3)) + 6*exp(-pi*i/3)*gamma(1/3)*hyper((1/3, 1/3), (4/3,), 46656/15625)/(25*gamma(4/3))
Respuesta numérica [src] 
0.284682676634811
0.284682676634811

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

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