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Resolución de integrales/ arctan/ tan(2x)/ abs(x^2arctan(2x))

Integral de abs(x^2arctan(2x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  121                  
  ---                  
  100                  
   /                   
  |                    
  |   | 2          |   
  |   |x *atan(2*x)| dx
  |                    
 /                     
-121                   
-----                  
 100
∫−121100121100∣x2atan⁡(2x)∣ dx\int\limits_{- \frac{121}{100}}^{\frac{121}{100}} \left|{x^{2} \operatorname{atan}{\left(2 x \right)}}\right|\, dx 
Integral(Abs(x^2*atan(2*x)), (x, -121/100, 121/100))
Respuesta [src] 
  121                                                                         
  ---                                                                         
  100                                                                         
   /                                                                          
  |                                                                           
  |   /                                           3                           
  |   |  x    2                  x             2*x                            
  |   |- - + x *atan(2*x) + ------------ + ------------  for atan(2*x) >= 0   
  |   |  6                    /       2\     /       2\                       
  |   |                     6*\1 + 4*x /   3*\1 + 4*x /                       
  |   <                                                                     dx
  |   |                           3                                           
  |   | x    2                 2*x             x                              
  |   | - - x *atan(2*x) - ------------ - ------------       otherwise        
  |   | 6                    /       2\     /       2\                        
  |   \                    3*\1 + 4*x /   6*\1 + 4*x /                        
  |                                                                           
 /                                                                            
-121                                                                          
-----                                                                         
 100
∫−121100121100{2x33(4x2+1)+x2atan⁡(2x)−x6+x6(4x2+1)for atan⁡(2x)≥0−2x33(4x2+1)−x2atan⁡(2x)+x6−x6(4x2+1)otherwise dx\int\limits_{- \frac{121}{100}}^{\frac{121}{100}} \begin{cases} \frac{2 x^{3}}{3 \left(4 x^{2} + 1\right)} + x^{2} \operatorname{atan}{\left(2 x \right)} - \frac{x}{6} + \frac{x}{6 \left(4 x^{2} + 1\right)} & \text{for}\: \operatorname{atan}{\left(2 x \right)} \geq 0 \\- \frac{2 x^{3}}{3 \left(4 x^{2} + 1\right)} - x^{2} \operatorname{atan}{\left(2 x \right)} + \frac{x}{6} - \frac{x}{6 \left(4 x^{2} + 1\right)} & \text{otherwise} \end{cases}\, dx 
=
= 
  121                                                                         
  ---                                                                         
  100                                                                         
   /                                                                          
  |                                                                           
  |   /                                           3                           
  |   |  x    2                  x             2*x                            
  |   |- - + x *atan(2*x) + ------------ + ------------  for atan(2*x) >= 0   
  |   |  6                    /       2\     /       2\                       
  |   |                     6*\1 + 4*x /   3*\1 + 4*x /                       
  |   <                                                                     dx
  |   |                           3                                           
  |   | x    2                 2*x             x                              
  |   | - - x *atan(2*x) - ------------ - ------------       otherwise        
  |   | 6                    /       2\     /       2\                        
  |   \                    3*\1 + 4*x /   6*\1 + 4*x /                        
  |                                                                           
 /                                                                            
-121                                                                          
-----                                                                         
 100
∫−121100121100{2x33(4x2+1)+x2atan⁡(2x)−x6+x6(4x2+1)for atan⁡(2x)≥0−2x33(4x2+1)−x2atan⁡(2x)+x6−x6(4x2+1)otherwise dx\int\limits_{- \frac{121}{100}}^{\frac{121}{100}} \begin{cases} \frac{2 x^{3}}{3 \left(4 x^{2} + 1\right)} + x^{2} \operatorname{atan}{\left(2 x \right)} - \frac{x}{6} + \frac{x}{6 \left(4 x^{2} + 1\right)} & \text{for}\: \operatorname{atan}{\left(2 x \right)} \geq 0 \\- \frac{2 x^{3}}{3 \left(4 x^{2} + 1\right)} - x^{2} \operatorname{atan}{\left(2 x \right)} + \frac{x}{6} - \frac{x}{6 \left(4 x^{2} + 1\right)} & \text{otherwise} \end{cases}\, dx 
Integral(Piecewise((-x/6 + x^2*atan(2*x) + x/(6*(1 + 4*x^2)) + 2*x^3/(3*(1 + 4*x^2)), atan(2*x) >= 0), (x/6 - x^2*atan(2*x) - 2*x^3/(3*(1 + 4*x^2)) - x/(6*(1 + 4*x^2)), True)), (x, -121/100, 121/100))
Respuesta numérica [src] 
1.22857882871821
1.22857882871821

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

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