Theorems · Theorem · real analysis
integral_mul_cpow_one_add_sq
∀ {a b : ℝ} {t : ℂ},
t ≠ -1 →
∫ (x : ℝ) in a..b, ↑x * (1 + ↑x ^ 2) ^ t =
(1 + ↑b ^ 2) ^ (t + 1) / (2 * (t + 1)) - (1 + ↑a ^ 2) ^ (t + 1) / (2 * (t + 1))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- mul_oneproof · cited by 3,885
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- Complex.ofRealstatement and proof · cited by 1,654
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
Cited by1
Results whose statement or proof uses this declaration.
- integral_mul_rpow_one_add_sqproof · cited by 0