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x*arctg^2(x)
Solving integrals/ x*arctg^2(x)

Integral of x*arctg^2(x) dx

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Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |        2      
 |  x*atan (x) dx
 |               
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0
$$\int\limits_{0}^{1} x \operatorname{atan}^{2}{\left(x \right)}\, dx$$ 
Integral(x*atan(x)^2, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                    
 |                         2         /     2\    2     2               
 |       2             atan (x)   log\1 + x /   x *atan (x)            
 | x*atan (x) dx = C + -------- + ----------- + ----------- - x*atan(x)
 |                        2            2             2                 
/
$$\int x \operatorname{atan}^{2}{\left(x \right)}\, dx = C + \frac{x^{2} \operatorname{atan}^{2}{\left(x \right)}}{2} - x \operatorname{atan}{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                2
log(2)   pi   pi 
------ - -- + ---
  2      4     16
$$- \frac{\pi}{4} + \frac{\log{\left(2 \right)}}{2} + \frac{\pi^{2}}{16}$$ 
=
= 
                2
log(2)   pi   pi 
------ - -- + ---
  2      4     16
$$- \frac{\pi}{4} + \frac{\log{\left(2 \right)}}{2} + \frac{\pi^{2}}{16}$$ 
log(2)/2 - pi/4 + pi^2/16
Numerical answer [src] 
0.178025701950609
0.178025701950609
The graph
Integral of x*arctg^2(x) dx

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

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