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Resolución de integrales/ log(x)/ e^(3*x)/ e^(3*x)*log(x)/x

Integral de e^(3*x)*log(x)/x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |   3*x          
 |  E   *log(x)   
 |  ----------- dx
 |       x        
 |                
/                 
0
∫01e3xlog⁡(x)x dx\int\limits_{0}^{1} \frac{e^{3 x} \log{\left(x \right)}}{x}\, dx 
Integral((E^(3*x)*log(x))/x, (x, 0, 1))
Respuesta (Indefinida) [src] 
                        //                                          2                                                _                                                                     \                 
                        ||                                       log (x)                                            |_  /1, 1, 1 |    \                                                    |                 
                        ||                                       ------- + EulerGamma*log(x) + log(3)*log(x) + 3*x* |   |        | 3*x|                                         for |x| < 1|                 
  /                     ||                                          2                                              3  3 \2, 2, 2 |    /                                                    |                 
 |                      ||                                                                                                                                                                 |                 
 |  3*x                 ||                            2                                                _                                                                                   |                 
 | E   *log(x)          ||                         log (x)                                            |_  /1, 1, 1 |    \                         /1\                                1     |                 
 | ----------- dx = C - |<                         ------- + EulerGamma*log(x) + log(3)*log(x) + 3*x* |   |        | 3*x| + pi*I*log(x) + pi*I*log|-|                           for --- < 1| + Ei(3*x)*log(x)
 |      x               ||                            2                                              3  3 \2, 2, 2 |    /                         \x/                               |x|    |                 
 |                      ||                                                                                                                                                                 |                 
/                       ||   2                                                _                                                                                                            |                 
                        ||log (x)                                            |_  /1, 1, 1 |    \                       __2, 0 /      1, 1 |  \         __0, 2 /1, 1       |  \             |                 
                        ||------- + EulerGamma*log(x) + log(3)*log(x) + 3*x* |   |        | 3*x| + pi*I*log(x) + pi*I*/__     |           | x| - pi*I*/__     |           | x|   otherwise |                 
                        ||   2                                              3  3 \2, 2, 2 |    /                      \_|2, 2 \0, 0       |  /        \_|2, 2 \      0, 0 |  /             |                 
                        \\                                                                                                                                                                 /
∫e3xlog⁡(x)x dx=C−{3x3F3(1,1,12,2,2|3x)+log⁡(x)22+γlog⁡(x)+log⁡(3)log⁡(x)for ∣x∣<13x3F3(1,1,12,2,2|3x)+iπlog⁡(1x)+log⁡(x)22+γlog⁡(x)+log⁡(3)log⁡(x)+iπlog⁡(x)for 1∣x∣<13x3F3(1,1,12,2,2|3x)+iπG2,22,0(1,10,0|x)−iπG2,20,2(1,10,0|x)+log⁡(x)22+γlog⁡(x)+log⁡(3)log⁡(x)+iπlog⁡(x)otherwise+log⁡(x)Ei⁡(3x)\int \frac{e^{3 x} \log{\left(x \right)}}{x}\, dx = C - \begin{cases} 3 x {{}_{3}F_{3}\left(\begin{matrix} 1, 1, 1 \\ 2, 2, 2 \end{matrix}\middle| {3 x} \right)} + \frac{\log{\left(x \right)}^{2}}{2} + \gamma \log{\left(x \right)} + \log{\left(3 \right)} \log{\left(x \right)} & \text{for}\: \left|{x}\right| < 1 \\3 x {{}_{3}F_{3}\left(\begin{matrix} 1, 1, 1 \\ 2, 2, 2 \end{matrix}\middle| {3 x} \right)} + i \pi \log{\left(\frac{1}{x} \right)} + \frac{\log{\left(x \right)}^{2}}{2} + \gamma \log{\left(x \right)} + \log{\left(3 \right)} \log{\left(x \right)} + i \pi \log{\left(x \right)} & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\3 x {{}_{3}F_{3}\left(\begin{matrix} 1, 1, 1 \\ 2, 2, 2 \end{matrix}\middle| {3 x} \right)} + i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix} & 1, 1 \\0, 0 & \end{matrix} \middle| {x} \right)} - i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 & \\ & 0, 0 \end{matrix} \middle| {x} \right)} + \frac{\log{\left(x \right)}^{2}}{2} + \gamma \log{\left(x \right)} + \log{\left(3 \right)} \log{\left(x \right)} + i \pi \log{\left(x \right)} & \text{otherwise} \end{cases} + \log{\left(x \right)} \operatorname{Ei}{\left(3 x \right)}
Simplificar
Respuesta [src] 
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nan
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nan
Respuesta numérica [src] 
-976.921202751545
-976.921202751545

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

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