have := integral_rpow (a := a) (b := b) (r := -c-1) (Or.inr ⟨by simp [h.1], h.2⟩)
a b c : ℝ
apos : 0 < a
a_lt_b : a < b
h : c ≠ 0 ∧ 0 ∉ [[a, b]]
⊢ ∫ (x : ℝ) in a..b, 1 / x ^ (c + 1) = (b ^ (-c) - a ^ (-c)) / -c
a b c : ℝ
apos : 0 < a
a_lt_b : a < b
h : c ≠ 0 ∧ 0 ∉ [[a, b]]
this : ∫ (x : ℝ) in a..b, x ^ (-c - 1) = (b ^ (-c - 1 + 1) - a ^ (-c - 1 + 1)) / (-c - 1 + 1)
⊢ ∫ (x : ℝ) in a..b, 1 / x ^ (c + 1) = (b ^ (-c) - a ^ (-c)) / -c