apply PartialIntegration f g fDiff gDiff fDerivgInt gDerivfInt lim_at_zero lim_at_inf
𝕂 : Type u_1
inst✝ : _root_.RCLike 𝕂
a b : ℝ
f g : ℝ → ℂ
ha : 0 < a
h : a ≤ b
fSupp : Function.support f ⊆ Icc a b
fDiff : DifferentiableOn ℝ f (Ioi 0)
gDiff : DifferentiableOn ℝ g (Ioi 0)
fderivCont : ContinuousOn (deriv f) (Ioi 0)
gderivCont : ContinuousOn (deriv g) (Ioi 0)
Icc_sub : Icc a b ⊆ Ioi 0
fderivSupp : Function.support (deriv f) ⊆ Icc a b
fgSupp : Function.support (f * g) ⊆ Icc a b
fDerivgInt : IntegrableOn (f * deriv g) (Ioi 0) volume
gDerivfInt : IntegrableOn (deriv f * g) (Ioi 0) volume
lim_at_zero : Tendsto (f * g) (𝓝[>] 0) (𝓝 0)
lim_at_inf : Tendsto (f * g) atTop (𝓝 0)
⊢ ∫ (x : ℝ) in Ioi 0, f x * deriv g x = -∫ (x : ℝ) in Ioi 0, deriv f x * g x
no goals