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Resolución de integrales/ (x-1)/ sqrt(1+((x-1)^3)^2)

Integral de sqrt(1+((x-1)^3)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  5                         
  /                         
 |                          
 |      _________________   
 |     /               2    
 |    /      /       3\     
 |  \/   1 + \(x - 1) /   dx
 |                          
/                           
2
$$\int\limits_{2}^{5} \sqrt{\left(\left(x - 1\right)^{3}\right)^{2} + 1}\, dx$$ 
Integral(sqrt(1 + ((x - 1)^3)^2), (x, 2, 5))
Respuesta (Indefinida) [src] 
  /                                                                                     
 |                                                      _                               
 |     _________________                               |_  /-1/2, 1/6 |         6  pi*I\
 |    /               2           (-1 + x)*Gamma(1/6)* |   |          | (-1 + x) *e    |
 |   /      /       3\                                2  1 \   7/6    |                /
 | \/   1 + \(x - 1) /   dx = C + ------------------------------------------------------
 |                                                     6*Gamma(7/6)                     
/
$$\int \sqrt{\left(\left(x - 1\right)^{3}\right)^{2} + 1}\, dx = C + \frac{\left(x - 1\right) \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {\left(x - 1\right)^{6} e^{i \pi}} \right)}}{6 \Gamma\left(\frac{7}{6}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
               _                                    _                          
              |_  /-1/2, 1/6 |   \                 |_  /-1/2, 1/6 |       pi*I\
  Gamma(1/6)* |   |          | -1|   2*Gamma(1/6)* |   |          | 4096*e    |
             2  1 \   7/6    |   /                2  1 \   7/6    |           /
- -------------------------------- + ------------------------------------------
            6*Gamma(7/6)                            3*Gamma(7/6)
$$- \frac{\Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {-1} \right)}}{6 \Gamma\left(\frac{7}{6}\right)} + \frac{2 \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {4096 e^{i \pi}} \right)}}{3 \Gamma\left(\frac{7}{6}\right)}$$ 
=
= 
               _                                    _                          
              |_  /-1/2, 1/6 |   \                 |_  /-1/2, 1/6 |       pi*I\
  Gamma(1/6)* |   |          | -1|   2*Gamma(1/6)* |   |          | 4096*e    |
             2  1 \   7/6    |   /                2  1 \   7/6    |           /
- -------------------------------- + ------------------------------------------
            6*Gamma(7/6)                            3*Gamma(7/6)
$$- \frac{\Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {-1} \right)}}{6 \Gamma\left(\frac{7}{6}\right)} + \frac{2 \Gamma\left(\frac{1}{6}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{6} \\ \frac{7}{6} \end{matrix}\middle| {4096 e^{i \pi}} \right)}}{3 \Gamma\left(\frac{7}{6}\right)}$$ 
-gamma(1/6)*hyper((-1/2, 1/6), (7/6,), -1)/(6*gamma(7/6)) + 2*gamma(1/6)*hyper((-1/2, 1/6), (7/6,), 4096*exp_polar(pi*i))/(3*gamma(7/6))
Respuesta numérica [src] 
63.9719234387983
63.9719234387983

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

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