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Integrating arctangent by parts

MediumCalculus~5m

Compute ∫01arctan⁡x dx\displaystyle\int_0^1 \arctan x\,dx. (to 4 decimals)

Show hints (2)+
  1. Integrate by parts with u=arctan⁡xu=\arctan x, dv=dxdv=dx.
  2. The remaining ∫x1+x2dx\int\frac{x}{1+x^2}dx is 12ln⁡(1+x2)\frac12\ln(1+x^2) by substitution.

Answer

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0.4388 (± 0.001)

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Asked at: Jane Street

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