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arctg(x)/(x^2+1)
Solving integrals/ arctg(x)/(x^2+1)

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

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
 oo           
  /           
 |            
 |  atan(x)   
 |  ------- dx
 |    2       
 |   x  + 1   
 |            
/             
1
∫1∞atan⁡(x)x2+1 dx\int\limits_{1}^{\infty} \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\, dx 
Integral(atan(x)/(x^2 + 1), (x, 1, oo))
Detail solution

  1. Let u=atan⁡(x)u = \operatorname{atan}{\left(x \right)}.

    Then let du=dxx2+1du = \frac{dx}{x^{2} + 1} and substitute dudu:

    ∫u du\int u\, du

    1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫u du=u22\int u\, du = \frac{u^{2}}{2}

    Now substitute uu back in:

    atan⁡2(x)2\frac{\operatorname{atan}^{2}{\left(x \right)}}{2}

  2. Add the constant of integration:

    atan⁡2(x)2+constant\frac{\operatorname{atan}^{2}{\left(x \right)}}{2}+ \mathrm{constant}

The answer is:

atan⁡2(x)2+constant\frac{\operatorname{atan}^{2}{\left(x \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                         
 |                      2   
 | atan(x)          atan (x)
 | ------- dx = C + --------
 |   2                 2    
 |  x  + 1                  
 |                          
/
∫atan⁡(x)x2+1 dx=C+atan⁡2(x)2\int \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\, dx = C + \frac{\operatorname{atan}^{2}{\left(x \right)}}{2}
Simplify
The graph
1.00001.01001.00101.00201.00301.00401.00501.00601.00701.00801.009002
Plot the graph f(x)
The answer [src] 
    2
3*pi 
-----
  32
3π232\frac{3 \pi^{2}}{32} 
=
= 
    2
3*pi 
-----
  32
3π232\frac{3 \pi^{2}}{32} 
3*pi^2/32
The graph
Integral of arctg(x)/(x^2+1) dx

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

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