Sr Examen

Otras calculadoras

Resolución de integrales/ x^3-8/ 1/(x^3-8)^(1/5)

Integral de 1/(x^3-8)^(1/5) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  4               
  /               
 |                
 |       1        
 |  ----------- dx
 |     ________   
 |  5 /  3        
 |  \/  x  - 8    
 |                
/                 
3
$$\int\limits_{3}^{4} \frac{1}{\sqrt[5]{x^{3} - 8}}\, dx$$ 
Integral(1/((x^3 - 8)^(1/5)), (x, 3, 4))
Respuesta (Indefinida) [src] 
                                -pi*I                                 
                                ------              _  /         |  3\
  /                        2/5    5                |_  |1/5, 1/3 | x |
 |                      x*2   *e      *Gamma(1/3)* |   |         | --|
 |      1                                         2  1 \  4/3    | 8 /
 | ----------- dx = C + ----------------------------------------------
 |    ________                           6*Gamma(4/3)                 
 | 5 /  3                                                             
 | \/  x  - 8                                                         
 |                                                                    
/
$$\int \frac{1}{\sqrt[5]{x^{3} - 8}}\, dx = C + \frac{2^{\frac{2}{5}} x e^{- \frac{i \pi}{5}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{3}}{8}} \right)}}{6 \Gamma\left(\frac{4}{3}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
        -pi*I                                              -pi*I                                
        ------              _                              ------              _                
   2/5    5                |_  /1/5, 1/3 |     \      2/5    5                |_  /1/5, 1/3 |  \
  2   *e      *Gamma(1/3)* |   |         | 27/8|   2*2   *e      *Gamma(1/3)* |   |         | 8|
                          2  1 \  4/3    |     /                             2  1 \  4/3    |  /
- ---------------------------------------------- + ---------------------------------------------
                   2*Gamma(4/3)                                     3*Gamma(4/3)
$$- \frac{2^{\frac{2}{5}} e^{- \frac{i \pi}{5}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{27}{8}} \right)}}{2 \Gamma\left(\frac{4}{3}\right)} + \frac{2 \cdot 2^{\frac{2}{5}} e^{- \frac{i \pi}{5}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {8} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$ 
=
= 
        -pi*I                                              -pi*I                                
        ------              _                              ------              _                
   2/5    5                |_  /1/5, 1/3 |     \      2/5    5                |_  /1/5, 1/3 |  \
  2   *e      *Gamma(1/3)* |   |         | 27/8|   2*2   *e      *Gamma(1/3)* |   |         | 8|
                          2  1 \  4/3    |     /                             2  1 \  4/3    |  /
- ---------------------------------------------- + ---------------------------------------------
                   2*Gamma(4/3)                                     3*Gamma(4/3)
$$- \frac{2^{\frac{2}{5}} e^{- \frac{i \pi}{5}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{27}{8}} \right)}}{2 \Gamma\left(\frac{4}{3}\right)} + \frac{2 \cdot 2^{\frac{2}{5}} e^{- \frac{i \pi}{5}} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {8} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$ 
-2^(2/5)*exp(-pi*i/5)*gamma(1/3)*hyper((1/5, 1/3), (4/3,), 27/8)/(2*gamma(4/3)) + 2*2^(2/5)*exp(-pi*i/5)*gamma(1/3)*hyper((1/5, 1/3), (4/3,), 8)/(3*gamma(4/3))
Respuesta numérica [src] 
0.494570011826401
0.494570011826401

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

    © Sr Examen