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  "body": "\n## Summary\n\nThe inverse tangent integral $\\operatorname{Ti}_2$ is the function $x \\mapsto \\int_0^x \\frac{\\arctan t}{t} \\, dt$.\nIt is the analogue of the [[dilogarithm|G0X0NWSDB7]] built from the [[arctangent|0CE768XNVP]] instead of the logarithm.\nFor real $x$ it equals the imaginary part of $\\operatorname{Li}_2(ix)$.\nIts value at $1$ is Catalan's constant.\n\n## Explanations\n\n### L1 human\n\nThe dilogarithm can be written as an integral of $-\\log(1 - t)/t$.\nReplace the logarithm by the arctangent and you get the inverse tangent integral.\nIts power series is $x - \\frac{x^3}{9} + \\frac{x^5}{25} - \\cdots$, with odd powers and squared odd numbers in the denominators.\nAt $x = 1$ this gives $1 - \\frac19 + \\frac1{25} - \\cdots = G \\approx 0.91597$, Catalan's constant.\n",
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