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Resolución de integrales/ 1-x^4/ dx/sqrt/ dx/sqrt(1-x^4)

Integral de dx/sqrt(1-x^4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |     ________   
 |    /      4    
 |  \/  1 - x     
 |                
/                 
1/2
∫12111−x4 dx\int\limits_{\frac{1}{2}}^{1} \frac{1}{\sqrt{1 - x^{4}}}\, dx 
Integral(1/(sqrt(1 - x^4)), (x, 1/2, 1))
Respuesta (Indefinida) [src] 
                                       _                         
  /                                   |_  /1/4, 1/2 |  4  2*pi*I\
 |                      x*Gamma(1/4)* |   |         | x *e      |
 |      1                            2  1 \  5/4    |           /
 | ----------- dx = C + -----------------------------------------
 |    ________                         4*Gamma(5/4)              
 |   /      4                                                    
 | \/  1 - x                                                     
 |                                                               
/
∫11−x4 dx=C+xΓ(14)2F1(14,1254|x4e2iπ)4Γ(54)\int \frac{1}{\sqrt{1 - 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| {x^{4} e^{2 i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}
Simplificar
Gráfica
0.501.000.550.600.650.700.750.800.850.900.950100
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    |  /
- --------------------------------- + ------------------------------
             8*Gamma(5/4)                      4*Gamma(5/4)
−Γ(14)2F1(14,1254|116)8Γ(54)+Γ(14)2F1(14,1254|1)4Γ(54)- \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)}}{8 \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)}}{4 \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    |  /
- --------------------------------- + ------------------------------
             8*Gamma(5/4)                      4*Gamma(5/4)
−Γ(14)2F1(14,1254|116)8Γ(54)+Γ(14)2F1(14,1254|1)4Γ(54)- \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)}}{8 \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)}}{4 \Gamma\left(\frac{5}{4}\right)} 
-gamma(1/4)*hyper((1/4, 1/2), (5/4,), 1/16)/(8*gamma(5/4)) + gamma(1/4)*hyper((1/4, 1/2), (5/4,), 1)/(4*gamma(5/4))
Respuesta numérica [src] 
0.807819333781177
0.807819333781177

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

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