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Resolución de integrales/ (1/3)/ x^2-1/ sin(x)/ sin(x)/(|x^2-16|)^(1/3)

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)∣x2−16∣3 dx\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)∣x2−16∣3 dx=C+∫sin⁡(x)∣x2−16∣3 dx\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
Simplificar
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)x−43x+43for x2−16≥0sin⁡(x)4−x3x+43otherwise dx\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)x−43x+43for x2−16≥0sin⁡(x)4−x3x+43otherwise dx\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.

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