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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo               
  /               
 |                
 |     log(x)     
 |  ----------- dx
 |     ________   
 |    /  3        
 |  \/  x  + 3    
 |                
/                 
1
∫1∞log⁡(x)x3+3 dx\int\limits_{1}^{\infty} \frac{\log{\left(x \right)}}{\sqrt{x^{3} + 3}}\, dx 
Integral(log(x)/sqrt(x^3 + 3), (x, 1, oo))
Respuesta (Indefinida) [src] 
  /                       /              
 |                       |               
 |    log(x)             |    log(x)     
 | ----------- dx = C +  | ----------- dx
 |    ________           |    ________   
 |   /  3                |   /      3    
 | \/  x  + 3            | \/  3 + x     
 |                       |               
/                       /
∫log⁡(x)x3+3 dx=C+∫log⁡(x)x3+3 dx\int \frac{\log{\left(x \right)}}{\sqrt{x^{3} + 3}}\, dx = C + \int \frac{\log{\left(x \right)}}{\sqrt{x^{3} + 3}}\, dx
Simplificar
Respuesta [src] 
              _                           
     2       |_  /1/6, 1/6, 1/2 |    pi*I\
Gamma (1/6)* |   |              | 3*e    |
            3  2 \   7/6, 7/6   |        /
------------------------------------------
                     2                    
              9*Gamma (7/6)
Γ2(16)3F2(16,16,1276,76|3eiπ)9Γ2(76)\frac{\Gamma^{2}\left(\frac{1}{6}\right) {{}_{3}F_{2}\left(\begin{matrix} \frac{1}{6}, \frac{1}{6}, \frac{1}{2} \\ \frac{7}{6}, \frac{7}{6} \end{matrix}\middle| {3 e^{i \pi}} \right)}}{9 \Gamma^{2}\left(\frac{7}{6}\right)} 
=
= 
              _                           
     2       |_  /1/6, 1/6, 1/2 |    pi*I\
Gamma (1/6)* |   |              | 3*e    |
            3  2 \   7/6, 7/6   |        /
------------------------------------------
                     2                    
              9*Gamma (7/6)
Γ2(16)3F2(16,16,1276,76|3eiπ)9Γ2(76)\frac{\Gamma^{2}\left(\frac{1}{6}\right) {{}_{3}F_{2}\left(\begin{matrix} \frac{1}{6}, \frac{1}{6}, \frac{1}{2} \\ \frac{7}{6}, \frac{7}{6} \end{matrix}\middle| {3 e^{i \pi}} \right)}}{9 \Gamma^{2}\left(\frac{7}{6}\right)} 
gamma(1/6)^2*hyper((1/6, 1/6, 1/2), (7/6, 7/6), 3*exp_polar(pi*i))/(9*gamma(7/6)^2)

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

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