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Integral de sin(x)/(|x^2-16|)^(1/3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  8                  
  /                  
 |                   
 |      sin(x)       
 |  -------------- dx
 |     ___________   
 |  3 / | 2     |    
 |  \/  |x  - 16|    
 |                   
/                    
0                    
08sin(x)x2163dx\int\limits_{0}^{8} \frac{\sin{\left(x \right)}}{\sqrt[3]{\left|{x^{2} - 16}\right|}}\, dx
Integral(sin(x)/|x^2 - 16|^(1/3), (x, 0, 8))
Respuesta (Indefinida) [src]
  /                          /                 
 |                          |                  
 |     sin(x)               |     sin(x)       
 | -------------- dx = C +  | -------------- dx
 |    ___________           |    ___________   
 | 3 / | 2     |            | 3 / | 2     |    
 | \/  |x  - 16|            | \/  |x  - 16|    
 |                          |                  
/                          /                   
sin(x)x2163dx=C+sin(x)x2163dx\int \frac{\sin{\left(x \right)}}{\sqrt[3]{\left|{x^{2} - 16}\right|}}\, dx = C + \int \frac{\sin{\left(x \right)}}{\sqrt[3]{\left|{x^{2} - 16}\right|}}\, dx
Respuesta [src]
  8                                            
  /                                            
 |                                             
 |  /       sin(x)                    2        
 |  |--------------------  for -16 + x  >= 0   
 |  |3 ________ 3 _______                      
 |  |\/ -4 + x *\/ 4 + x                       
 |  <                                        dx
 |  |       sin(x)                             
 |  |-------------------       otherwise       
 |  |3 _______ 3 _______                       
 |  \\/ 4 + x *\/ 4 - x                        
 |                                             
/                                              
0                                              
08{sin(x)x43x+43forx2160sin(x)4x3x+43otherwisedx\int\limits_{0}^{8} \begin{cases} \frac{\sin{\left(x \right)}}{\sqrt[3]{x - 4} \sqrt[3]{x + 4}} & \text{for}\: x^{2} - 16 \geq 0 \\\frac{\sin{\left(x \right)}}{\sqrt[3]{4 - x} \sqrt[3]{x + 4}} & \text{otherwise} \end{cases}\, dx
=
=
  8                                            
  /                                            
 |                                             
 |  /       sin(x)                    2        
 |  |--------------------  for -16 + x  >= 0   
 |  |3 ________ 3 _______                      
 |  |\/ -4 + x *\/ 4 + x                       
 |  <                                        dx
 |  |       sin(x)                             
 |  |-------------------       otherwise       
 |  |3 _______ 3 _______                       
 |  \\/ 4 + x *\/ 4 - x                        
 |                                             
/                                              
0                                              
08{sin(x)x43x+43forx2160sin(x)4x3x+43otherwisedx\int\limits_{0}^{8} \begin{cases} \frac{\sin{\left(x \right)}}{\sqrt[3]{x - 4} \sqrt[3]{x + 4}} & \text{for}\: x^{2} - 16 \geq 0 \\\frac{\sin{\left(x \right)}}{\sqrt[3]{4 - x} \sqrt[3]{x + 4}} & \text{otherwise} \end{cases}\, dx
Integral(Piecewise((sin(x)/((-4 + x)^(1/3)*(4 + x)^(1/3)), -16 + x^2 >= 0), (sin(x)/((4 + x)^(1/3)*(4 - x)^(1/3)), True)), (x, 0, 8))

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