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Resolución de integrales/ 6-x^4/ 1/(256-x^4)^(1/2)

Integral de 1/(256-x^4)^(1/2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  4                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |     __________   
 |    /        4    
 |  \/  256 - x     
 |                  
/                   
2
$$\int\limits_{2}^{4} \frac{1}{\sqrt{256 - x^{4}}}\, dx$$ 
Integral(1/(sqrt(256 - x^4)), (x, 2, 4))
Respuesta (Indefinida) [src] 
                                                                   
                                         _  /         |  4  2*pi*I\
  /                                     |_  |1/4, 1/2 | x *e      |
 |                        x*Gamma(1/4)* |   |         | ----------|
 |       1                             2  1 \  5/4    |    256    /
 | ------------- dx = C + -----------------------------------------
 |    __________                        64*Gamma(5/4)              
 |   /        4                                                    
 | \/  256 - x                                                     
 |                                                                 
/
$$\int \frac{1}{\sqrt{256 - x^{4}}}\, dx = C + \frac{x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{x^{4} e^{2 i \pi}}{256}} \right)}}{64 \Gamma\left(\frac{5}{4}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
               _                                   _                
              |_  /1/4, 1/2 |     \               |_  /1/4, 1/2 |  \
  Gamma(1/4)* |   |         | 1/16|   Gamma(1/4)* |   |         | 1|
             2  1 \  5/4    |     /              2  1 \  5/4    |  /
- --------------------------------- + ------------------------------
            32*Gamma(5/4)                     16*Gamma(5/4)
$$- \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{1}{16}} \right)}}{32 \Gamma\left(\frac{5}{4}\right)} + \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {1} \right)}}{16 \Gamma\left(\frac{5}{4}\right)}$$ 
=
= 
               _                                   _                
              |_  /1/4, 1/2 |     \               |_  /1/4, 1/2 |  \
  Gamma(1/4)* |   |         | 1/16|   Gamma(1/4)* |   |         | 1|
             2  1 \  5/4    |     /              2  1 \  5/4    |  /
- --------------------------------- + ------------------------------
            32*Gamma(5/4)                     16*Gamma(5/4)
$$- \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {\frac{1}{16}} \right)}}{32 \Gamma\left(\frac{5}{4}\right)} + \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {1} \right)}}{16 \Gamma\left(\frac{5}{4}\right)}$$ 
-gamma(1/4)*hyper((1/4, 1/2), (5/4,), 1/16)/(32*gamma(5/4)) + gamma(1/4)*hyper((1/4, 1/2), (5/4,), 1)/(16*gamma(5/4))
Respuesta numérica [src] 
0.201954833445294
0.201954833445294

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

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