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Resolución de integrales/ x^4*dx/ dx/sqrt/ x^4*dx/sqrt(x^10-3)

Integral de x^4*dx/sqrt(x^10-3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |        4        
 |       x         
 |  ------------ dx
 |     _________   
 |    /  10        
 |  \/  x   - 3    
 |                 
/                  
0
∫01x4x10−3 dx\int\limits_{0}^{1} \frac{x^{4}}{\sqrt{x^{10} - 3}}\, dx 
Integral(x^4/sqrt(x^10 - 3), (x, 0, 1))
Respuesta (Indefinida) [src] 
                         //      /  ___  5\                 \
                         ||      |\/ 3 *x |                 |
  /                      || acosh|--------|        | 10|    |
 |                       ||      \   3    /        |x  |    |
 |       4               || ---------------    for ----- > 1|
 |      x                ||        5                 3      |
 | ------------ dx = C + |<                                 |
 |    _________          ||       /  ___  5\                |
 |   /  10               ||       |\/ 3 *x |                |
 | \/  x   - 3           ||-I*asin|--------|                |
 |                       ||       \   3    /                |
/                        ||------------------    otherwise  |
                         \\        5                        /
∫x4x10−3 dx=C+{acosh⁡(3x53)5for ∣x10∣3>1−iasin⁡(3x53)5otherwise\int \frac{x^{4}}{\sqrt{x^{10} - 3}}\, dx = C + \begin{cases} \frac{\operatorname{acosh}{\left(\frac{\sqrt{3} x^{5}}{3} \right)}}{5} & \text{for}\: \frac{\left|{x^{10}}\right|}{3} > 1 \\- \frac{i \operatorname{asin}{\left(\frac{\sqrt{3} x^{5}}{3} \right)}}{5} & \text{otherwise} \end{cases}
Simplificar
Gráfica
0.000000.000020.000040.000060.000080.000100.000120.000140.000160.000180.0002001
Trazar el gráfico f(x)
Respuesta [src] 
  1                                   
  /                                   
 |                                    
 |  /       ___  4           10       
 |  |     \/ 3 *x           x         
 |  |-----------------  for --- > 1   
 |  |       __________       3        
 |  |      /       10                 
 |  |     /       x                   
 |  |3*  /   -1 + ---                 
 |  |  \/          3                  
 |  <                               dx
 |  |       ___  4                    
 |  |  -I*\/ 3 *x                     
 |  |----------------    otherwise    
 |  |       _________                 
 |  |      /      10                  
 |  |     /      x                    
 |  |3*  /   1 - ---                  
 |  \  \/         3                   
 |                                    
/                                     
0
∫01{3x43x103−1for x103>1−3ix431−x103otherwise dx\int\limits_{0}^{1} \begin{cases} \frac{\sqrt{3} x^{4}}{3 \sqrt{\frac{x^{10}}{3} - 1}} & \text{for}\: \frac{x^{10}}{3} > 1 \\- \frac{\sqrt{3} i x^{4}}{3 \sqrt{1 - \frac{x^{10}}{3}}} & \text{otherwise} \end{cases}\, dx 
=
= 
  1                                   
  /                                   
 |                                    
 |  /       ___  4           10       
 |  |     \/ 3 *x           x         
 |  |-----------------  for --- > 1   
 |  |       __________       3        
 |  |      /       10                 
 |  |     /       x                   
 |  |3*  /   -1 + ---                 
 |  |  \/          3                  
 |  <                               dx
 |  |       ___  4                    
 |  |  -I*\/ 3 *x                     
 |  |----------------    otherwise    
 |  |       _________                 
 |  |      /      10                  
 |  |     /      x                    
 |  |3*  /   1 - ---                  
 |  \  \/         3                   
 |                                    
/                                     
0
∫01{3x43x103−1for x103>1−3ix431−x103otherwise dx\int\limits_{0}^{1} \begin{cases} \frac{\sqrt{3} x^{4}}{3 \sqrt{\frac{x^{10}}{3} - 1}} & \text{for}\: \frac{x^{10}}{3} > 1 \\- \frac{\sqrt{3} i x^{4}}{3 \sqrt{1 - \frac{x^{10}}{3}}} & \text{otherwise} \end{cases}\, dx 
Integral(Piecewise((sqrt(3)*x^4/(3*sqrt(-1 + x^10/3)), x^10/3 > 1), (-i*sqrt(3)*x^4/(3*sqrt(1 - x^10/3)), True)), (x, 0, 1))
Respuesta numérica [src] 
(0.0 - 0.123095941734077j)
(0.0 - 0.123095941734077j)

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

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