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Resolución de integrales/ sqrt(2+(1/(4t^4)))

Integral de sqrt(2+(1/(4t^4))) dt

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  3                   
  /                   
 |                    
 |       __________   
 |      /      1      
 |     /  2 + ----  dt
 |    /          4    
 |  \/        4*t     
 |                    
/                     
1
$$\int\limits_{1}^{3} \sqrt{2 + \frac{1}{4 t^{4}}}\, dt$$ 
Integral(sqrt(2 + 1/(4*t^4)), (t, 1, 3))
Respuesta (Indefinida) [src] 
                                                                         
                                                  _  /           |  pi*I\
  /                             ___              |_  |-1/2, -1/4 | e    |
 |                          t*\/ 2 *Gamma(-1/4)* |   |           | -----|
 |      __________                              2  1 |   3/4     |     4|
 |     /      1                                      \           |  8*t /
 |    /  2 + ----  dt = C - ---------------------------------------------
 |   /          4                            4*Gamma(3/4)                
 | \/        4*t                                                         
 |                                                                       
/
$$\int \sqrt{2 + \frac{1}{4 t^{4}}}\, dt = C - \frac{\sqrt{2} t \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {\frac{e^{i \pi}}{8 t^{4}}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                        _                                              _                     
      ___              |_  /-1/2, -1/4 |       \     ___              |_  /-1/2, -1/4 |     \
  3*\/ 2 *Gamma(-1/4)* |   |           | -1/648|   \/ 2 *Gamma(-1/4)* |   |           | -1/8|
                      2  1 \   3/4     |       /                     2  1 \   3/4     |     /
- ---------------------------------------------- + ------------------------------------------
                   4*Gamma(3/4)                                   4*Gamma(3/4)
$$\frac{\sqrt{2} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {- \frac{1}{8}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)} - \frac{3 \sqrt{2} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {- \frac{1}{648}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}$$ 
=
= 
                        _                                              _                     
      ___              |_  /-1/2, -1/4 |       \     ___              |_  /-1/2, -1/4 |     \
  3*\/ 2 *Gamma(-1/4)* |   |           | -1/648|   \/ 2 *Gamma(-1/4)* |   |           | -1/8|
                      2  1 \   3/4     |       /                     2  1 \   3/4     |     /
- ---------------------------------------------- + ------------------------------------------
                   4*Gamma(3/4)                                   4*Gamma(3/4)
$$\frac{\sqrt{2} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {- \frac{1}{8}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)} - \frac{3 \sqrt{2} \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, - \frac{1}{4} \\ \frac{3}{4} \end{matrix}\middle| {- \frac{1}{648}} \right)}}{4 \Gamma\left(\frac{3}{4}\right)}$$ 
-3*sqrt(2)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), -1/648)/(4*gamma(3/4)) + sqrt(2)*gamma(-1/4)*hyper((-1/2, -1/4), (3/4,), -1/8)/(4*gamma(3/4))
Respuesta numérica [src] 
2.85641913511826
2.85641913511826

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