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Resolución de integrales/ sin(2*x)/ sin(2*x)/sqrt(x^3+4)

Integral de sin(2*x)/sqrt(x^3+4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo               
  /               
 |                
 |    sin(2*x)    
 |  ----------- dx
 |     ________   
 |    /  3        
 |  \/  x  + 4    
 |                
/                 
0
∫0∞sin⁡(2x)x3+4 dx\int\limits_{0}^{\infty} \frac{\sin{\left(2 x \right)}}{\sqrt{x^{3} + 4}}\, dx 
Integral(sin(2*x)/sqrt(x^3 + 4), (x, 0, oo))
Respuesta (Indefinida) [src] 
  /                         /                
 |                         |                 
 |   sin(2*x)              | cos(x)*sin(x)   
 | ----------- dx = C + 2* | ------------- dx
 |    ________             |     ________    
 |   /  3                  |    /      3     
 | \/  x  + 4              |  \/  4 + x      
 |                         |                 
/                         /
∫sin⁡(2x)x3+4 dx=C+2∫sin⁡(x)cos⁡(x)x3+4 dx\int \frac{\sin{\left(2 x \right)}}{\sqrt{x^{3} + 4}}\, dx = C + 2 \int \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{x^{3} + 4}}\, dx
Simplificar
Respuesta [src] 
6 ___   ___  __5, 2 /        5/6, 1/3                       |  16\
\/ 2 *\/ 3 */__     |                                       | ---|
            \_|2, 8 \7/12, 1/12, 1/6, 1/2, 5/6  0, 1/3, 2/3 | 729/
------------------------------------------------------------------
                              12*pi
263G2,85,2(56,13712,112,16,12,560,13,23|16729)12π\frac{\sqrt[6]{2} \sqrt{3} {G_{2, 8}^{5, 2}\left(\begin{matrix} \frac{5}{6}, \frac{1}{3} & \\\frac{7}{12}, \frac{1}{12}, \frac{1}{6}, \frac{1}{2}, \frac{5}{6} & 0, \frac{1}{3}, \frac{2}{3} \end{matrix} \middle| {\frac{16}{729}} \right)}}{12 \pi} 
=
= 
6 ___   ___  __5, 2 /        5/6, 1/3                       |  16\
\/ 2 *\/ 3 */__     |                                       | ---|
            \_|2, 8 \7/12, 1/12, 1/6, 1/2, 5/6  0, 1/3, 2/3 | 729/
------------------------------------------------------------------
                              12*pi
263G2,85,2(56,13712,112,16,12,560,13,23|16729)12π\frac{\sqrt[6]{2} \sqrt{3} {G_{2, 8}^{5, 2}\left(\begin{matrix} \frac{5}{6}, \frac{1}{3} & \\\frac{7}{12}, \frac{1}{12}, \frac{1}{6}, \frac{1}{2}, \frac{5}{6} & 0, \frac{1}{3}, \frac{2}{3} \end{matrix} \middle| {\frac{16}{729}} \right)}}{12 \pi} 
2^(1/6)*sqrt(3)*meijerg(((5/6, 1/3), ()), ((7/12, 1/12, 1/6, 1/2, 5/6), (0, 1/3, 2/3)), 16/729)/(12*pi)

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

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