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Resolución de integrales/ x^3+8/ sqrt(x^3+8)

Integral de sqrt(x^3+8) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 11               
  /               
 |                
 |     ________   
 |    /  3        
 |  \/  x  + 8  dx
 |                
/                 
1
∫111x3+8 dx\int\limits_{1}^{11} \sqrt{x^{3} + 8}\, dx 
Integral(sqrt(x^3 + 8), (x, 1, 11))
Respuesta (Indefinida) [src] 
                                                                        
  /                                            _  /          |  3  pi*I\
 |                            ___             |_  |-1/2, 1/3 | x *e    |
 |    ________          2*x*\/ 2 *Gamma(1/3)* |   |          | --------|
 |   /  3                                    2  1 \   4/3    |    8    /
 | \/  x  + 8  dx = C + ------------------------------------------------
 |                                        3*Gamma(4/3)                  
/
∫x3+8 dx=C+22xΓ(13)2F1(−12,1343|x3eiπ8)3Γ(43)\int \sqrt{x^{3} + 8}\, dx = C + \frac{2 \sqrt{2} x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{3} e^{i \pi}}{8}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}
Simplificar
Gráfica
1.02.03.04.05.06.07.08.09.011.010.00200
Trazar el gráfico f(x)
Respuesta [src] 
                                                                                                
                       _                                             _  /          |       pi*I\
      ___             |_  /-1/2, 1/3 |     \        ___             |_  |-1/2, 1/3 | 1331*e    |
  2*\/ 2 *Gamma(1/3)* |   |          | -1/8|   22*\/ 2 *Gamma(1/3)* |   |          | ----------|
                     2  1 \   4/3    |     /                       2  1 \   4/3    |     8     /
- ------------------------------------------ + -------------------------------------------------
                 3*Gamma(4/3)                                     3*Gamma(4/3)
−22Γ(13)2F1(−12,1343|−18)3Γ(43)+222Γ(13)2F1(−12,1343|1331eiπ8)3Γ(43)- \frac{2 \sqrt{2} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {- \frac{1}{8}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{22 \sqrt{2} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{1331 e^{i \pi}}{8}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} 
=
= 
                                                                                                
                       _                                             _  /          |       pi*I\
      ___             |_  /-1/2, 1/3 |     \        ___             |_  |-1/2, 1/3 | 1331*e    |
  2*\/ 2 *Gamma(1/3)* |   |          | -1/8|   22*\/ 2 *Gamma(1/3)* |   |          | ----------|
                     2  1 \   4/3    |     /                       2  1 \   4/3    |     8     /
- ------------------------------------------ + -------------------------------------------------
                 3*Gamma(4/3)                                     3*Gamma(4/3)
−22Γ(13)2F1(−12,1343|−18)3Γ(43)+222Γ(13)2F1(−12,1343|1331eiπ8)3Γ(43)- \frac{2 \sqrt{2} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {- \frac{1}{8}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} + \frac{22 \sqrt{2} \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{2}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{1331 e^{i \pi}}{8}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} 
-2*sqrt(2)*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), -1/8)/(3*gamma(4/3)) + 22*sqrt(2)*gamma(1/3)*hyper((-1/2, 1/3), (4/3,), 1331*exp_polar(pi*i)/8)/(3*gamma(4/3))
Respuesta numérica [src] 
164.759529099392
164.759529099392

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

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