Theorems · Theorem · real analysis
integral_Iic_inv_one_add_sq
∀ {i : ℝ}, ∫ (x : ℝ) in Set.Iic i, (1 + x ^ 2)⁻¹ = Real.arctan i + Real.pi / 2- Cited by
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- Foundations
- Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasureTheory.integralstatement · cited by 1,779
- Real.pistatement and proof · cited by 1,774
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- Set.Iicstatement and proof · cited by 1,111
- sub_neg_eq_addproof · cited by 264
- Real.arctanstatement and proof · cited by 111
- MeasureTheory.Integrable.integrableOnproof · cited by 74
- tendsto_nhds_of_tendsto_nhdsWithinproof · cited by 9
- Real.hasDerivAt_arctan'proof · cited by 3
- integrable_inv_one_add_sqproof · cited by 3
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