Sr Examen

Otras calculadoras

Resolución de integrales/ (1/3)/ 1/((27-x^3)^(1/3))

Integral de 1/((27-x^3)^(1/3)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  3                
  /                
 |                 
 |       1         
 |  ------------ dx
 |     _________   
 |  3 /       3    
 |  \/  27 - x     
 |                 
/                  
2
$$\int\limits_{2}^{3} \frac{1}{\sqrt[3]{27 - x^{3}}}\, dx$$ 
Integral(1/((27 - x^3)^(1/3)), (x, 2, 3))
Respuesta (Indefinida) [src] 
                                                                  
                                        _  /         |  3  2*pi*I\
  /                                    |_  |1/3, 1/3 | x *e      |
 |                       x*Gamma(1/3)* |   |         | ----------|
 |      1                             2  1 \  4/3    |     27    /
 | ------------ dx = C + -----------------------------------------
 |    _________                         9*Gamma(4/3)              
 | 3 /       3                                                    
 | \/  27 - x                                                     
 |                                                                
/
$$\int \frac{1}{\sqrt[3]{27 - x^{3}}}\, dx = C + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{x^{3} e^{2 i \pi}}{27}} \right)}}{9 \Gamma\left(\frac{4}{3}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                 _                                   _                
                |_  /1/3, 1/3 |     \               |_  /1/3, 1/3 |  \
  2*Gamma(1/3)* |   |         | 8/27|   Gamma(1/3)* |   |         | 1|
               2  1 \  4/3    |     /              2  1 \  4/3    |  /
- ----------------------------------- + ------------------------------
              9*Gamma(4/3)                       3*Gamma(4/3)
$$- \frac{2 \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{8}{27}} \right)}}{9 \Gamma\left(\frac{4}{3}\right)} + \frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {1} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$ 
=
= 
                 _                                   _                
                |_  /1/3, 1/3 |     \               |_  /1/3, 1/3 |  \
  2*Gamma(1/3)* |   |         | 8/27|   Gamma(1/3)* |   |         | 1|
               2  1 \  4/3    |     /              2  1 \  4/3    |  /
- ----------------------------------- + ------------------------------
              9*Gamma(4/3)                       3*Gamma(4/3)
$$- \frac{2 \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {\frac{8}{27}} \right)}}{9 \Gamma\left(\frac{4}{3}\right)} + \frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{3} \\ \frac{4}{3} \end{matrix}\middle| {1} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}$$ 
-2*gamma(1/3)*hyper((1/3, 1/3), (4/3,), 8/27)/(9*gamma(4/3)) + gamma(1/3)*hyper((1/3, 1/3), (4/3,), 1)/(3*gamma(4/3))
Respuesta numérica [src] 
0.523842008673909
0.523842008673909

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

    © Sr Examen