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You entered:

arctgx^2x/(1+x^2)

What you mean?

Integral of arctgx^2x/(1+x^2) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src]
  1              
  /              
 |               
 |      2        
 |  acot (x)*x   
 |  ---------- dx
 |         2     
 |    1 + x      
 |               
/                
0                
$$\int\limits_{0}^{1} \frac{x \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1}\, dx$$
Integral(acot(x)^2*x/(1 + x^2), (x, 0, 1))
The answer (Indefinite) [src]
  /                      /             
 |                      |              
 |     2                |       2      
 | acot (x)*x           | x*acot (x)   
 | ---------- dx = C +  | ---------- dx
 |        2             |        2     
 |   1 + x              |   1 + x      
 |                      |              
/                      /               
$$\int {{{x\,\left({\rm arccot}\; x\right)^2}\over{x^2+1}}}{\;dx}$$
The answer [src]
  1              
  /              
 |               
 |        2      
 |  x*acot (x)   
 |  ---------- dx
 |         2     
 |    1 + x      
 |               
/                
0                
$$\int_{0}^{1}{{{x\,\left({\rm arccot}\; x\right)^2}\over{x^2+1}}\;dx }$$
=
=
  1              
  /              
 |               
 |        2      
 |  x*acot (x)   
 |  ---------- dx
 |         2     
 |    1 + x      
 |               
/                
0                
$$\int\limits_{0}^{1} \frac{x \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1}\, dx$$
Numerical answer [src]
0.382665484717462
0.382665484717462

    Use the examples entering the upper and lower limits of integration.