Theorems · Theorem · real analysis
integral_inv_sq_add_sq
∀ {a b c : ℝ}, c ≠ 0 → ∫ (x : ℝ) in a..b, (c ^ 2 + x ^ 2)⁻¹ = c⁻¹ * (Real.arctan (b / c) - Real.arctan (a / c))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- one_ne_zeroproof · cited by 885
- div_oneproof · cited by 629
- intervalIntegralstatement and proof · cited by 546
- Real.arctanstatement and proof · cited by 111
- intervalIntegral.integral_const_mulproof · cited by 29
- intervalIntegral.integral_comp_divproof · cited by 4
- integral_inv_one_add_sqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- integral_div_sq_add_sqproof · cited by 0