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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  8                 
  /                 
 |                  
 |     __________   
 |    /        4    
 |  \/  1 + 9*x   dx
 |                  
/                   
1
∫189x4+1 dx\int\limits_{1}^{8} \sqrt{9 x^{4} + 1}\, dx 
Integral(sqrt(1 + 9*x^4), (x, 1, 8))
Respuesta (Indefinida) [src] 
  /                                      _                          
 |                                      |_  /-1/2, 1/4 |    4  pi*I\
 |    __________          x*Gamma(1/4)* |   |          | 9*x *e    |
 |   /        4                        2  1 \   5/4    |           /
 | \/  1 + 9*x   dx = C + ------------------------------------------
 |                                       4*Gamma(5/4)               
/
∫9x4+1 dx=C+xΓ(14)2F1(−12,1454|9x4eiπ)4Γ(54)\int \sqrt{9 x^{4} + 1}\, dx = C + \frac{x \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 x^{4} e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)}
Simplificar
Gráfica
1.08.01.52.02.53.03.54.04.55.05.56.06.57.07.501000
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    |   Gamma(1/4)* |   |          | 9*e    |
             2  1 \   5/4    |            /              2  1 \   5/4    |        /
------------------------------------------- - -------------------------------------
                 Gamma(5/4)                                4*Gamma(5/4)
−Γ(14)2F1(−12,1454|9eiπ)4Γ(54)+2Γ(14)2F1(−12,1454|36864eiπ)Γ(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| {9 e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \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)} 
=
= 
               _                                           _                       
              |_  /-1/2, 1/4 |        pi*I\               |_  /-1/2, 1/4 |    pi*I\
2*Gamma(1/4)* |   |          | 36864*e    |   Gamma(1/4)* |   |          | 9*e    |
             2  1 \   5/4    |            /              2  1 \   5/4    |        /
------------------------------------------- - -------------------------------------
                 Gamma(5/4)                                4*Gamma(5/4)
−Γ(14)2F1(−12,1454|9eiπ)4Γ(54)+2Γ(14)2F1(−12,1454|36864eiπ)Γ(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| {9 e^{i \pi}} \right)}}{4 \Gamma\left(\frac{5}{4}\right)} + \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)} 
2*gamma(1/4)*hyper((-1/2, 1/4), (5/4,), 36864*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] 
511.144934716265
511.144934716265

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

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