theorem extracted_formal_statement_9.{u_1} {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : Measure Ω}
  [inst : IsFiniteMeasure μ] {X : Ω → ℝ} (t b : ℝ) (ht : t > 0) (hX : AEMeasurable X μ) (hb : ∀ᵐ (ω : Ω) ∂μ, X ω ≤ b)
  (hm1 : HasFiniteIntegral (fun ω => rexp (t * X ω)) μ) : Integrable (fun ω => rexp (t * X ω)) μ := sorry

State before:
Ω : Type u_1
m : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsFiniteMeasure μ
X : Ω → ℝ
t b : ℝ
ht : t > 0
hX : AEMeasurable X μ
hb : ∀ᵐ (ω : Ω) ∂μ, X ω ≤ b
hm1 : HasFiniteIntegral (fun ω => rexp (t * X ω)) μ
⊢ Integrable (fun ω => rexp (t * X ω)) μ

Tactic: exact
  ⟨aestronglyMeasurable_iff_aemeasurable.mpr <| measurable_exp.comp_aemeasurable' (hX.const_mul t), hm1⟩

State after:

Relevant lemmas: