Question

Find the indefinite integral.
(e^(4 x) + e^(-5 x)) dx

Answer 1

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 !