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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  3               
  /               
 |                
 |       1        
 |  ----------- dx
 |     ________   
 |    /      5    
 |  \/  3 - x     
 |                
/                 
1
$$\int\limits_{1}^{3} \frac{1}{\sqrt{3 - x^{5}}}\, dx$$ 
Integral(1/(sqrt(3 - x^5)), (x, 1, 3))
Respuesta (Indefinida) [src] 
                                                                       
                                             _  /         |  5  2*pi*I\
  /                         ___             |_  |1/5, 1/2 | x *e      |
 |                      x*\/ 3 *Gamma(1/5)* |   |         | ----------|
 |      1                                  2  1 \  6/5    |     3     /
 | ----------- dx = C + -----------------------------------------------
 |    ________                           15*Gamma(6/5)                 
 |   /      5                                                          
 | \/  3 - x                                                           
 |                                                                     
/
$$\int \frac{1}{\sqrt{3 - x^{5}}}\, dx = C + \frac{\sqrt{3} x \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{2} \\ \frac{6}{5} \end{matrix}\middle| {\frac{x^{5} e^{2 i \pi}}{3}} \right)}}{15 \Gamma\left(\frac{6}{5}\right)}$$
Simplificar
Respuesta [src] 
                     _                                        _                         
    ___             |_  /1/5, 1/2 |    \     ___             |_  /1/5, 1/2 |     2*pi*I\
  \/ 3 *Gamma(1/5)* |   |         | 1/3|   \/ 3 *Gamma(1/5)* |   |         | 81*e      |
                   2  1 \  6/5    |    /                    2  1 \  6/5    |           /
- -------------------------------------- + ---------------------------------------------
              15*Gamma(6/5)                                 5*Gamma(6/5)
$$- \frac{\sqrt{3} \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{2} \\ \frac{6}{5} \end{matrix}\middle| {\frac{1}{3}} \right)}}{15 \Gamma\left(\frac{6}{5}\right)} + \frac{\sqrt{3} \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{2} \\ \frac{6}{5} \end{matrix}\middle| {81 e^{2 i \pi}} \right)}}{5 \Gamma\left(\frac{6}{5}\right)}$$ 
=
= 
                     _                                        _                         
    ___             |_  /1/5, 1/2 |    \     ___             |_  /1/5, 1/2 |     2*pi*I\
  \/ 3 *Gamma(1/5)* |   |         | 1/3|   \/ 3 *Gamma(1/5)* |   |         | 81*e      |
                   2  1 \  6/5    |    /                    2  1 \  6/5    |           /
- -------------------------------------- + ---------------------------------------------
              15*Gamma(6/5)                                 5*Gamma(6/5)
$$- \frac{\sqrt{3} \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{2} \\ \frac{6}{5} \end{matrix}\middle| {\frac{1}{3}} \right)}}{15 \Gamma\left(\frac{6}{5}\right)} + \frac{\sqrt{3} \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{2} \\ \frac{6}{5} \end{matrix}\middle| {81 e^{2 i \pi}} \right)}}{5 \Gamma\left(\frac{6}{5}\right)}$$ 
-sqrt(3)*gamma(1/5)*hyper((1/5, 1/2), (6/5,), 1/3)/(15*gamma(6/5)) + sqrt(3)*gamma(1/5)*hyper((1/5, 1/2), (6/5,), 81*exp_polar(2*pi*i))/(5*gamma(6/5))
Respuesta numérica [src] 
(0.323796494698494 - 0.488505378537082j)
(0.323796494698494 - 0.488505378537082j)

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

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