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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  5                       
  /                       
 |                        
 |     ________________   
 |    /              4    
 |  \/  1 + 9*(x - 1)   dx
 |                        
/                         
2
$$\int\limits_{2}^{5} \sqrt{9 \left(x - 1\right)^{4} + 1}\, dx$$ 
Integral(sqrt(1 + 9*(x - 1)^4), (x, 2, 5))
Respuesta (Indefinida) [src] 
  /                                                   _                                 
 |                                                   |_  /-1/2, 1/4 |           4  pi*I\
 |    ________________          (-1 + x)*Gamma(1/4)* |   |          | 9*(-1 + x) *e    |
 |   /              4                               2  1 \   5/4    |                  /
 | \/  1 + 9*(x - 1)   dx = C + --------------------------------------------------------
 |                                                    4*Gamma(5/4)                      
/
$$\int \sqrt{9 \left(x - 1\right)^{4} + 1}\, dx = C + \frac{\left(x - 1\right) \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {9 \left(x - 1\right)^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
             _                                          _                       
            |_  /-1/2, 1/4 |       pi*I\               |_  /-1/2, 1/4 |    pi*I\
Gamma(1/4)* |   |          | 2304*e    |   Gamma(1/4)* |   |          | 9*e    |
           2  1 \   5/4    |           /              2  1 \   5/4    |        /
---------------------------------------- - -------------------------------------
               Gamma(5/4)                               4*Gamma(5/4)
$$- \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {9 e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {2304 e^{i \pi}} \right)}}{\Gamma\left(\frac{5}{4}\right)}$$ 
=
= 
             _                                          _                       
            |_  /-1/2, 1/4 |       pi*I\               |_  /-1/2, 1/4 |    pi*I\
Gamma(1/4)* |   |          | 2304*e    |   Gamma(1/4)* |   |          | 9*e    |
           2  1 \   5/4    |           /              2  1 \   5/4    |        /
---------------------------------------- - -------------------------------------
               Gamma(5/4)                               4*Gamma(5/4)
$$- \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {9 e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{4} \\ \frac{5}{4} \end{matrix}\middle| {2304 e^{i \pi}} \right)}}{\Gamma\left(\frac{5}{4}\right)}$$ 
gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 2304*exp_polar(pi*i))/gamma(5/4) - gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 9*exp_polar(pi*i))/(4*gamma(5/4))
Respuesta numérica [src] 
63.1241022587903
63.1241022587903

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

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