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Resolución de integrales/ Inx/x/ sinInx/x

Integral de sinInx/x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  E                 
  /                 
 |                  
 |  sin(x)*log(x)   
 |  ------------- dx
 |        x         
 |                  
/                   
1
∫1elog⁡(x)sin⁡(x)x dx\int\limits_{1}^{e} \frac{\log{\left(x \right)} \sin{\left(x \right)}}{x}\, dx 
Integral((sin(x)*log(x))/x, (x, 1, E))
Respuesta (Indefinida) [src] 
  /                                                                   
 |                                           _  /              |   2 \
 | sin(x)*log(x)                            |_  |   1/2, 1/2   | -x  |
 | ------------- dx = C + Si(x)*log(x) - x* |   |              | ----|
 |       x                                 2  3 \3/2, 3/2, 3/2 |  4  /
 |                                                                    
/
∫log⁡(x)sin⁡(x)x dx=C−x2F3(12,1232,32,32|−x24)+log⁡(x)Si⁡(x)\int \frac{\log{\left(x \right)} \sin{\left(x \right)}}{x}\, dx = C - x {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{x^{2}}{4}} \right)} + \log{\left(x \right)} \operatorname{Si}{\left(x \right)}
Simplificar
Gráfica
1.01.21.41.61.82.02.22.42.61-2
Trazar el gráfico f(x)
Respuesta [src] 
                                                                     
      _  /              |   2 \             _                        
     |_  |   1/2, 1/2   | -e  |            |_  /   1/2, 1/2   |     \
- E* |   |              | ----| + Si(E) +  |   |              | -1/4|
    2  3 \3/2, 3/2, 3/2 |  4  /           2  3 \3/2, 3/2, 3/2 |     /
2F3(12,1232,32,32|−14)−e2F3(12,1232,32,32|−e24)+Si⁡(e){{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)} - e {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{e^{2}}{4}} \right)} + \operatorname{Si}{\left(e \right)} 
=
= 
                                                                     
      _  /              |   2 \             _                        
     |_  |   1/2, 1/2   | -e  |            |_  /   1/2, 1/2   |     \
- E* |   |              | ----| + Si(E) +  |   |              | -1/4|
    2  3 \3/2, 3/2, 3/2 |  4  /           2  3 \3/2, 3/2, 3/2 |     /
2F3(12,1232,32,32|−14)−e2F3(12,1232,32,32|−e24)+Si⁡(e){{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{1}{4}} \right)} - e {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2} \\ \frac{3}{2}, \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {- \frac{e^{2}}{4}} \right)} + \operatorname{Si}{\left(e \right)} 
-E*hyper((1/2, 1/2), (3/2, 3/2, 3/2), -exp(2)/4) + Si(E) + hyper((1/2, 1/2), (3/2, 3/2, 3/2), -1/4)
Respuesta numérica [src] 
0.411229412828585
0.411229412828585

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

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