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xarctg(x/2)
Solving integrals/ xarctg(x/2)

Integral of xarctg(x/2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |        /x\   
 |  x*atan|-| dx
 |        \2/   
 |              
/               
0
$$\int\limits_{0}^{1} x \operatorname{atan}{\left(\frac{x}{2} \right)}\, dx$$ 
Integral(x*atan(x/2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                    2     /x\
 |                                    x *atan|-|
 |       /x\                    /x\          \2/
 | x*atan|-| dx = C - x + 2*atan|-| + ----------
 |       \2/                    \2/       2     
 |                                              
/
$$\int x \operatorname{atan}{\left(\frac{x}{2} \right)}\, dx = C + \frac{x^{2} \operatorname{atan}{\left(\frac{x}{2} \right)}}{2} - x + 2 \operatorname{atan}{\left(\frac{x}{2} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     5*atan(1/2)
-1 + -----------
          2
$$-1 + \frac{5 \operatorname{atan}{\left(\frac{1}{2} \right)}}{2}$$ 
=
= 
     5*atan(1/2)
-1 + -----------
          2
$$-1 + \frac{5 \operatorname{atan}{\left(\frac{1}{2} \right)}}{2}$$ 
-1 + 5*atan(1/2)/2
Numerical answer [src] 
0.159119022502015
0.159119022502015
The graph
Integral of xarctg(x/2) dx

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

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