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

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

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The solution

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∫01atan⁡(x)x2+1 dx\int\limits_{0}^{1} \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\, dx 
Integral(atan(x)/(1 + x^2), (x, 0, 1))
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] 
  /                         
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 | atan(x)          atan (x)
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 |  1 + x                   
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∫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
0.001.000.100.200.300.400.500.600.700.800.900.00.5
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Numerical answer [src] 
0.308425137534042
0.308425137534042
The graph
Integral of atan(x)/(1+x^2) dx

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

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