What is the most general antiderivative of f(x) = -6e^x + 6sec^2(x) where -pi/2< x < pi/2
To find the most general antiderivative of f(x) = -6e^x + 6sec^2(x) within the given interval, we need to integrate each term separately.
The antiderivative of -6e^x is -6e^x.
To find the antiderivative of 6sec^2(x), we can use the trigonometric identity: ∫sec^2(x) dx = tan(x) + C, where C is the constant of integration.
Therefore, the most general antiderivative of f(x) = -6e^x + 6sec^2(x) within the given interval is -6e^x + tan(x) + C, where C is the constant of integration.