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Resolución de integrales/ (sinx)/ (1+x)/ (3+x)/ (sinx)/((1+x)*(3+x))

Integral de (sinx)/((1+x)*(3+x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                   
  /                   
 |                    
 |       sin(x)       
 |  --------------- dx
 |  (1 + x)*(3 + x)   
 |                    
/                     
0
∫0∞sin⁡(x)(x+1)(x+3) dx\int\limits_{0}^{\infty} \frac{\sin{\left(x \right)}}{\left(x + 1\right) \left(x + 3\right)}\, dx 
Integral(sin(x)/(((1 + x)*(3 + x))), (x, 0, oo))
Respuesta (Indefinida) [src] 
  /                           /                  
 |                           |                   
 |      sin(x)               |      sin(x)       
 | --------------- dx = C +  | --------------- dx
 | (1 + x)*(3 + x)           | (1 + x)*(3 + x)   
 |                           |                   
/                           /
∫sin⁡(x)(x+1)(x+3) dx=C+∫sin⁡(x)(x+1)(x+3) dx\int \frac{\sin{\left(x \right)}}{\left(x + 1\right) \left(x + 3\right)}\, dx = C + \int \frac{\sin{\left(x \right)}}{\left(x + 1\right) \left(x + 3\right)}\, dx
Simplificar
Respuesta [src] 
   __2, 3 /0, -1/2, 0  1/2 |  \    __2, 3 /0, 0, 1/2  1/2 |    \
  /__     |                | 4|   /__     |               | 4/9|
  \_|4, 2 \ -1/2, 0        |  /   \_|4, 2 \ 0, 1/2        |    /
- ----------------------------- - ------------------------------
                 ____                            ____           
             2*\/ pi                         6*\/ pi
−G4,22,3(0,−12,012−12,0|4)2π−G4,22,3(0,0,12120,12|49)6π- \frac{{G_{4, 2}^{2, 3}\left(\begin{matrix} 0, - \frac{1}{2}, 0 & \frac{1}{2} \\- \frac{1}{2}, 0 & \end{matrix} \middle| {4} \right)}}{2 \sqrt{\pi}} - \frac{{G_{4, 2}^{2, 3}\left(\begin{matrix} 0, 0, \frac{1}{2} & \frac{1}{2} \\0, \frac{1}{2} & \end{matrix} \middle| {\frac{4}{9}} \right)}}{6 \sqrt{\pi}} 
=
= 
   __2, 3 /0, -1/2, 0  1/2 |  \    __2, 3 /0, 0, 1/2  1/2 |    \
  /__     |                | 4|   /__     |               | 4/9|
  \_|4, 2 \ -1/2, 0        |  /   \_|4, 2 \ 0, 1/2        |    /
- ----------------------------- - ------------------------------
                 ____                            ____           
             2*\/ pi                         6*\/ pi
−G4,22,3(0,−12,012−12,0|4)2π−G4,22,3(0,0,12120,12|49)6π- \frac{{G_{4, 2}^{2, 3}\left(\begin{matrix} 0, - \frac{1}{2}, 0 & \frac{1}{2} \\- \frac{1}{2}, 0 & \end{matrix} \middle| {4} \right)}}{2 \sqrt{\pi}} - \frac{{G_{4, 2}^{2, 3}\left(\begin{matrix} 0, 0, \frac{1}{2} & \frac{1}{2} \\0, \frac{1}{2} & \end{matrix} \middle| {\frac{4}{9}} \right)}}{6 \sqrt{\pi}} 
-meijerg(((0, -1/2, 0), (1/2,)), ((-1/2, 0), ()), 4)/(2*sqrt(pi)) - meijerg(((0, 0, 1/2), (1/2,)), ((0, 1/2), ()), 4/9)/(6*sqrt(pi))

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

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