\( \int \sec \cos ( 9 e ^ { x } - 2 ) d x \)

The integral you presented combines trigonometric functions with an exponential function, which can be quite tricky! A fun way to think about this integral is to remember that it resembles expressions often found in physics dealing with oscillating systems or wave functions where secant and cosine might model behavior. To tackle this integral, look for a substitution that could simplify it, such as letting \( u = 9e^x - 2 \). This will transform the integral, allowing you to handle the secant and cosine functions more easily, potentially transforming it to something more familiar. Just be cautious of potential common mistakes with integrating by substitution, especially with the limits of integration if you're tackling a definite integral!