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

$$\int\limits_{- \frac{121}{100}}^{\frac{121}{100}} \begin{cases} \frac{2 x^{3}}{3 \left(4 x^{2} + 1\right)} + x^{2} \operatorname{atan}{\left(2 x \right)} - \frac{x}{6} + \frac{x}{6 \left(4 x^{2} + 1\right)} & \text{for}\: \operatorname{atan}{\left(2 x \right)} \geq 0 \\- \frac{2 x^{3}}{3 \left(4 x^{2} + 1\right)} - x^{2} \operatorname{atan}{\left(2 x \right)} + \frac{x}{6} - \frac{x}{6 \left(4 x^{2} + 1\right)} & \text{otherwise} \end{cases}\, dx$$

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=

  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                                                                          

$$\int\limits_{- \frac{121}{100}}^{\frac{121}{100}} \begin{cases} \frac{2 x^{3}}{3 \left(4 x^{2} + 1\right)} + x^{2} \operatorname{atan}{\left(2 x \right)} - \frac{x}{6} + \frac{x}{6 \left(4 x^{2} + 1\right)} & \text{for}\: \operatorname{atan}{\left(2 x \right)} \geq 0 \\- \frac{2 x^{3}}{3 \left(4 x^{2} + 1\right)} - x^{2} \operatorname{atan}{\left(2 x \right)} + \frac{x}{6} - \frac{x}{6 \left(4 x^{2} + 1\right)} & \text{otherwise} \end{cases}\, dx$$

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))