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Solving integrals/ arctgx/2dx

Integral of arctgx/2dx dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |  acot(x)   
 |  ------- dx
 |     2      
 |            
/             
0
∫01acot⁡(x)2 dx\int\limits_{0}^{1} \frac{\operatorname{acot}{\left(x \right)}}{2}\, dx 
Integral(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:

    ∫acot⁡(x)2 dx=∫acot⁡(x) dx2\int \frac{\operatorname{acot}{\left(x \right)}}{2}\, dx = \frac{\int \operatorname{acot}{\left(x \right)}\, dx}{2}

    1. Don't know the steps in finding this integral.

      But the integral is

      xacot⁡(x)+log⁡(x2+1)2x \operatorname{acot}{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2}

    So, the result is: xacot⁡(x)2+log⁡(x2+1)4\frac{x \operatorname{acot}{\left(x \right)}}{2} + \frac{\log{\left(x^{2} + 1 \right)}}{4}

  2. Add the constant of integration:

    xacot⁡(x)2+log⁡(x2+1)4+constant\frac{x \operatorname{acot}{\left(x \right)}}{2} + \frac{\log{\left(x^{2} + 1 \right)}}{4}+ \mathrm{constant}

The answer is:

xacot⁡(x)2+log⁡(x2+1)4+constant\frac{x \operatorname{acot}{\left(x \right)}}{2} + \frac{\log{\left(x^{2} + 1 \right)}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                        
 |                     /     2\            
 | acot(x)          log\1 + x /   x*acot(x)
 | ------- dx = C + ----------- + ---------
 |    2                  4            2    
 |                                         
/
∫acot⁡(x)2 dx=C+xacot⁡(x)2+log⁡(x2+1)4\int \frac{\operatorname{acot}{\left(x \right)}}{2}\, dx = C + \frac{x \operatorname{acot}{\left(x \right)}}{2} + \frac{\log{\left(x^{2} + 1 \right)}}{4}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Plot the graph f(x)
The answer [src] 
log(2)   pi
------ + --
  4      8
log⁡(2)4+π8\frac{\log{\left(2 \right)}}{4} + \frac{\pi}{8} 
=
= 
log(2)   pi
------ + --
  4      8
log⁡(2)4+π8\frac{\log{\left(2 \right)}}{4} + \frac{\pi}{8} 
log(2)/4 + pi/8
Numerical answer [src] 
0.56598587683871
0.56598587683871

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

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