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Integral de x^n/(1-x^4)^0.5 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1               
  /               
 |                
 |        n       
 |       x        
 |  ----------- dx
 |     ________   
 |    /      4    
 |  \/  1 - x     
 |                
/                 
0                 
$$\int\limits_{0}^{1} \frac{x^{n}}{\sqrt{1 - x^{4}}}\, dx$$
Integral(x^n/sqrt(1 - x^4), (x, 0, 1))
Respuesta (Indefinida) [src]
                                                                        
                                               /     1   n |           \
                                            _  |1/2, - + - |           |
                           n      /1   n\  |_  |     4   4 |  4  2*pi*I|
  /                     x*x *Gamma|- + -|* |   |           | x *e      |
 |                                \4   4/ 2  1 |  5   n    |           |
 |       n                                     |  - + -    |           |
 |      x                                      \  4   4    |           /
 | ----------- dx = C + ------------------------------------------------
 |    ________                                  /5   n\                 
 |   /      4                            4*Gamma|- + -|                 
 | \/  1 - x                                    \4   4/                 
 |                                                                      
/                                                                       
$$\int \frac{x^{n}}{\sqrt{1 - x^{4}}}\, dx = C + \frac{x x^{n} \Gamma\left(\frac{n}{4} + \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{n}{4} + \frac{1}{4} \\ \frac{n}{4} + \frac{5}{4} \end{matrix}\middle| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{n}{4} + \frac{5}{4}\right)}$$
Respuesta [src]
                                  
                  /     1   n |  \
               _  |1/2, - + - |  |
     /1   n\  |_  |     4   4 |  |
Gamma|- + -|* |   |           | 1|
     \4   4/ 2  1 |  5   n    |  |
                  |  - + -    |  |
                  \  4   4    |  /
----------------------------------
                 /5   n\          
          4*Gamma|- + -|          
                 \4   4/          
$$\frac{\Gamma\left(\frac{n}{4} + \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{n}{4} + \frac{1}{4} \\ \frac{n}{4} + \frac{5}{4} \end{matrix}\middle| {1} \right)}}{4 \Gamma\left(\frac{n}{4} + \frac{5}{4}\right)}$$
=
=
                                  
                  /     1   n |  \
               _  |1/2, - + - |  |
     /1   n\  |_  |     4   4 |  |
Gamma|- + -|* |   |           | 1|
     \4   4/ 2  1 |  5   n    |  |
                  |  - + -    |  |
                  \  4   4    |  /
----------------------------------
                 /5   n\          
          4*Gamma|- + -|          
                 \4   4/          
$$\frac{\Gamma\left(\frac{n}{4} + \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{n}{4} + \frac{1}{4} \\ \frac{n}{4} + \frac{5}{4} \end{matrix}\middle| {1} \right)}}{4 \Gamma\left(\frac{n}{4} + \frac{5}{4}\right)}$$
gamma(1/4 + n/4)*hyper((1/2, 1/4 + n/4), (5/4 + n/4,), 1)/(4*gamma(5/4 + n/4))

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