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Resolución de integrales/ 1/sqrt/ x^(5/2)/ 1/sqrt(1-7*(x^(5/2)))

Integral de 1/sqrt(1-7*(x^(5/2))) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |     ____________   
 |    /        5/2    
 |  \/  1 - 7*x       
 |                    
/                     
0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{1 - 7 x^{\frac{5}{2}}}}\, dx$$ 
Integral(1/(sqrt(1 - 7*x^(5/2))), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                             _                             
  /                                         |_  /2/5, 1/2 |    5/2  2*pi*I\
 |                          2*x*Gamma(2/5)* |   |         | 7*x   *e      |
 |        1                                2  1 \  7/5    |               /
 | --------------- dx = C + -----------------------------------------------
 |    ____________                            5*Gamma(7/5)                 
 |   /        5/2                                                          
 | \/  1 - 7*x                                                             
 |                                                                         
/
$$\int \frac{1}{\sqrt{1 - 7 x^{\frac{5}{2}}}}\, dx = C + \frac{2 x \Gamma\left(\frac{2}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{5}, \frac{1}{2} \\ \frac{7}{5} \end{matrix}\middle| {7 x^{\frac{5}{2}} e^{2 i \pi}} \right)}}{5 \Gamma\left(\frac{7}{5}\right)}$$
Simplificar
Respuesta [src] 
               _                        
              |_  /2/5, 1/2 |    2*pi*I\
2*Gamma(2/5)* |   |         | 7*e      |
             2  1 \  7/5    |          /
----------------------------------------
              5*Gamma(7/5)
$$\frac{2 \Gamma\left(\frac{2}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{5}, \frac{1}{2} \\ \frac{7}{5} \end{matrix}\middle| {7 e^{2 i \pi}} \right)}}{5 \Gamma\left(\frac{7}{5}\right)}$$ 
=
= 
               _                        
              |_  /2/5, 1/2 |    2*pi*I\
2*Gamma(2/5)* |   |         | 7*e      |
             2  1 \  7/5    |          /
----------------------------------------
              5*Gamma(7/5)
$$\frac{2 \Gamma\left(\frac{2}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{5}, \frac{1}{2} \\ \frac{7}{5} \end{matrix}\middle| {7 e^{2 i \pi}} \right)}}{5 \Gamma\left(\frac{7}{5}\right)}$$ 
2*gamma(2/5)*hyper((2/5, 1/2), (7/5,), 7*exp_polar(2*pi*i))/(5*gamma(7/5))
Respuesta numérica [src] 
(0.630753622900028 - 0.551587673563463j)
(0.630753622900028 - 0.551587673563463j)

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

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