Find the most general antiderivative of f(x)=−4e^x−1sec^2(x), where −π/2<x<π/2.

Question

Note: Any arbitrary constants used must be an upper-case "C".

Answer 1

since d/dx e^x = e^x
and d/dx tanx = sec^2 x
∫ -4 e^x - sec^2(x) dx = -4e^x - tan(x) + C
note that the domain was conveniently chosen to avoid the asymptotes.