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Resolución de integrales/ dx/((x^5+2)^1/3)

Integral de dx/((x^5+2)^1/3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo               
  /               
 |                
 |       1        
 |  ----------- dx
 |     ________   
 |  3 /  5        
 |  \/  x  + 2    
 |                
/                 
1
∫1∞1x5+23 dx\int\limits_{1}^{\infty} \frac{1}{\sqrt[3]{x^{5} + 2}}\, dx 
Integral(1/((x^5 + 2)^(1/3)), (x, 1, oo))
Respuesta (Indefinida) [src] 
                                                                    
                                            _  /         |  5  pi*I\
  /                        2/3             |_  |1/5, 1/3 | x *e    |
 |                      x*2   *Gamma(1/5)* |   |         | --------|
 |      1                                 2  1 \  6/5    |    2    /
 | ----------- dx = C + --------------------------------------------
 |    ________                         10*Gamma(6/5)                
 | 3 /  5                                                           
 | \/  x  + 2                                                       
 |                                                                  
/
∫1x5+23 dx=C+223xΓ(15)2F1(15,1365|x5eiπ2)10Γ(65)\int \frac{1}{\sqrt[3]{x^{5} + 2}}\, dx = C + \frac{2^{\frac{2}{3}} x \Gamma\left(\frac{1}{5}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{5}, \frac{1}{3} \\ \frac{6}{5} \end{matrix}\middle| {\frac{x^{5} e^{i \pi}}{2}} \right)}}{10 \Gamma\left(\frac{6}{5}\right)}
Simplificar
Respuesta [src] 
                                      
              _  /2/15, 1/3 |        \
             |_  |          |    pi*I|
Gamma(2/15)* |   |    17    | 2*e    |
            2  1 |    --    |        |
                 \    15    |        /
--------------------------------------
                    /17\              
             5*Gamma|--|              
                    \15/
Γ(215)2F1(215,131715|2eiπ)5Γ(1715)\frac{\Gamma\left(\frac{2}{15}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{15}, \frac{1}{3} \\ \frac{17}{15} \end{matrix}\middle| {2 e^{i \pi}} \right)}}{5 \Gamma\left(\frac{17}{15}\right)} 
=
= 
                                      
              _  /2/15, 1/3 |        \
             |_  |          |    pi*I|
Gamma(2/15)* |   |    17    | 2*e    |
            2  1 |    --    |        |
                 \    15    |        /
--------------------------------------
                    /17\              
             5*Gamma|--|              
                    \15/
Γ(215)2F1(215,131715|2eiπ)5Γ(1715)\frac{\Gamma\left(\frac{2}{15}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{2}{15}, \frac{1}{3} \\ \frac{17}{15} \end{matrix}\middle| {2 e^{i \pi}} \right)}}{5 \Gamma\left(\frac{17}{15}\right)} 
gamma(2/15)*hyper((2/15, 1/3), (17/15,), 2*exp_polar(pi*i))/(5*gamma(17/15))

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

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