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Resolución de integrales/ sqrt(1+9(-4-x)^4)

Integral de sqrt(1+9(-4-x)^4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  4                        
  /                        
 |                         
 |     _________________   
 |    /               4    
 |  \/  1 + 9*(-4 - x)   dx
 |                         
/                          
5
$$\int\limits_{5}^{4} \sqrt{9 \left(- x - 4\right)^{4} + 1}\, dx$$ 
Integral(sqrt(1 + 9*(-4 - x)^4), (x, 5, 4))
Respuesta (Indefinida) [src] 
  /                                                   _                                
 |                                                   |_  /-1/2, 1/4 |          4  pi*I\
 |    _________________          (4 + x)*Gamma(1/4)* |   |          | 9*(4 + x) *e    |
 |   /               4                              2  1 \   5/4    |                 /
 | \/  1 + 9*(-4 - x)   dx = C + ------------------------------------------------------
 |                                                    4*Gamma(5/4)                     
/
$$\int \sqrt{9 \left(- x - 4\right)^{4} + 1}\, dx = C + \frac{\left(x + 4\right) \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {9 \left(x + 4\right)^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
               _                                             _                           
              |_  /-1/2, 1/4 |        pi*I\                 |_  /-1/2, 1/4 |        pi*I\
2*Gamma(1/4)* |   |          | 36864*e    |   9*Gamma(1/4)* |   |          | 59049*e    |
             2  1 \   5/4    |            /                2  1 \   5/4    |            /
------------------------------------------- - -------------------------------------------
                 Gamma(5/4)                                   4*Gamma(5/4)
$$\frac{2 \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {36864 e^{i \pi}} \right)}}{\Gamma\left(\frac{5}{4}\right)} - \frac{9 \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {59049 e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$ 
=
= 
               _                                             _                           
              |_  /-1/2, 1/4 |        pi*I\                 |_  /-1/2, 1/4 |        pi*I\
2*Gamma(1/4)* |   |          | 36864*e    |   9*Gamma(1/4)* |   |          | 59049*e    |
             2  1 \   5/4    |            /                2  1 \   5/4    |            /
------------------------------------------- - -------------------------------------------
                 Gamma(5/4)                                   4*Gamma(5/4)
$$\frac{2 \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {36864 e^{i \pi}} \right)}}{\Gamma\left(\frac{5}{4}\right)} - \frac{9 \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {59049 e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$ 
2*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 36864*exp_polar(pi*i))/gamma(5/4) - 9*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 59049*exp_polar(pi*i))/(4*gamma(5/4))
Respuesta numérica [src] 
-217.002314802239
-217.002314802239

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

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