Find the most general antiderivative of the function. \[ f(\theta)=\sec (\theta) \tan (\theta)-5 e^{\theta} \] \( f(\theta)=\square \)

To find the most general antiderivative of the function \( f(\theta) = \sec(\theta) \tan(\theta) - 5 e^{\theta} \), we can integrate each term separately. The integral of \( \sec(\theta) \tan(\theta) \) is \( \sec(\theta) + C_1 \), where \( C_1 \) is a constant of integration. The integral of \( -5 e^{\theta} \) is \( -5 e^{\theta} + C_2 \), where \( C_2 \) is another constant. Combining these results, we have: \[ \int f(\theta) \, d\theta = \sec(\theta) - 5 e^{\theta} + C \] where \( C = C_1 + C_2 \) is the most general constant. Thus, the most general antiderivative is: \[ F(\theta) = \sec(\theta) - 5 e^{\theta} + C \]