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Resolución de integrales/ (3x-2)/ sqrt(1+(9*(3x-2)^2)^2)

Integral de sqrt(1+(9*(3x-2)^2)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                             
  /                             
 |                              
 |      _____________________   
 |     /                   2    
 |    /      /           2\     
 |  \/   1 + \9*(3*x - 2) /   dx
 |                              
/                               
0
∫01(9(3x−2)2)2+1 dx\int\limits_{0}^{1} \sqrt{\left(9 \left(3 x - 2\right)^{2}\right)^{2} + 1}\, dx 
Integral(sqrt(1 + (9*(3*x - 2)^2)^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                  
 |                                                            _                                      
 |     _____________________                                 |_  /-1/2, 1/4 |                4  pi*I\
 |    /                   2           (-2/3 + x)*Gamma(1/4)* |   |          | 6561*(-2/3 + x) *e    |
 |   /      /           2\                                  2  1 \   5/4    |                       /
 | \/   1 + \9*(3*x - 2) /   dx = C + ---------------------------------------------------------------
 |                                                              4*Gamma(5/4)                         
/
∫(9(3x−2)2)2+1 dx=C+(x−23)Γ(14)2F1(−12,1454|6561(x−23)4eiπ)4Γ(54)\int \sqrt{\left(9 \left(3 x - 2\right)^{2}\right)^{2} + 1}\, dx = C + \frac{\left(x - \frac{2}{3}\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| {6561 \left(x - \frac{2}{3}\right)^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}
Simplificar
Gráfica
0.02.00.20.40.60.81.01.21.41.61.8-200200
Trazar el gráfico f(x)
Respuesta [src] 
             _                                          _                        
            |_  /-1/2, 1/4 |       pi*I\               |_  /-1/2, 1/4 |     pi*I\
Gamma(1/4)* |   |          | 1296*e    |   Gamma(1/4)* |   |          | 81*e    |
           2  1 \   5/4    |           /              2  1 \   5/4    |         /
---------------------------------------- + --------------------------------------
              6*Gamma(5/4)                             12*Gamma(5/4)
Γ(14)2F1(−12,1454|81eiπ)12Γ(54)+Γ(14)2F1(−12,1454|1296eiπ)6Γ(54)\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| {81 e^{i \pi}} \right)}}{12 \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| {1296 e^{i \pi}} \right)}}{6 \Gamma\left(\frac{5}{4}\right)} 
=
= 
             _                                          _                        
            |_  /-1/2, 1/4 |       pi*I\               |_  /-1/2, 1/4 |     pi*I\
Gamma(1/4)* |   |          | 1296*e    |   Gamma(1/4)* |   |          | 81*e    |
           2  1 \   5/4    |           /              2  1 \   5/4    |         /
---------------------------------------- + --------------------------------------
              6*Gamma(5/4)                             12*Gamma(5/4)
Γ(14)2F1(−12,1454|81eiπ)12Γ(54)+Γ(14)2F1(−12,1454|1296eiπ)6Γ(54)\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| {81 e^{i \pi}} \right)}}{12 \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| {1296 e^{i \pi}} \right)}}{6 \Gamma\left(\frac{5}{4}\right)} 
gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 1296*exp_polar(pi*i))/(6*gamma(5/4)) + gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 81*exp_polar(pi*i))/(12*gamma(5/4))
Respuesta numérica [src] 
9.24691170153148
9.24691170153148

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

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