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x(arctgx/2)

Integral of x(arctgx/2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1             
  /             
 |              
 |  x*acot(x)   
 |  --------- dx
 |      2       
 |              
/               
0               
$$\int\limits_{0}^{1} \frac{x \operatorname{acot}{\left(x \right)}}{2}\, dx$$
Integral(x*acot(x)/2, (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Use integration by parts:

      Let and let .

      Then .

      To find :

      1. The integral of is when :

      Now evaluate the sub-integral.

    2. The integral of a constant times a function is the constant times the integral of the function:

      1. Rewrite the integrand:

      2. Integrate term-by-term:

        1. The integral of a constant is the constant times the variable of integration:

        1. The integral of a constant times a function is the constant times the integral of the function:

          1. The integral of is .

          So, the result is:

        The result is:

      So, the result is:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                           
 |                                   2        
 | x*acot(x)          atan(x)   x   x *acot(x)
 | --------- dx = C - ------- + - + ----------
 |     2                 4      4       4     
 |                                            
/                                             
$${{{{x-\arctan x}\over{2}}+{{x^2\,{\rm arccot}\; x}\over{2}}}\over{2 }}$$
The graph
The answer [src]
1/4
$${{1}\over{4}}$$
=
=
1/4
$$\frac{1}{4}$$
Numerical answer [src]
0.25
0.25
The graph
Integral of x(arctgx/2) dx

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