Question
Find the indefinite integral.
(e^(4 x) + e^(-5 x)) dx
(e^(4 x) + e^(-5 x)) dx
Answers
Steve
recall that ∫ e^u du = e^u
∫e^(4x) dx
let u = 4x, so du = 4 dx. That means that you have
∫e^(4x) (1/4)(4x dx) = ∫ 1/4 e^u du = 1/4 e^u = 1/4 (e^4x)
similarly, for any constant a,
∫e^(ax) dx = 1/a e^(ax)
and as always, don't forget the +C !
∫e^(4x) dx
let u = 4x, so du = 4 dx. That means that you have
∫e^(4x) (1/4)(4x dx) = ∫ 1/4 e^u du = 1/4 e^u = 1/4 (e^4x)
similarly, for any constant a,
∫e^(ax) dx = 1/a e^(ax)
and as always, don't forget the +C !