Indefinite Integration
Exponential and Trigonometric Functions
Grade 12
Question:
<p>Evaluate \(\int \frac{dx}{e^x \sec x(1 + \tan x)}\)</p>
<p>(a) \(e^x \cos x + C\)</p>
<p>(b) \(e^x \sec x + C\)</p>
<p>(c) \(e^x \sin x + C\)</p>
<p>(d) \(e^x \tan x + C\)</p>
Step-by-Step Solution
Key Concept: Recognize that the integral involves exponential and trigonometric functions where substitution simplifies the expression.
<p>The integral can be simplified by noting that $\frac{1}{\sec x} = \cos x$. Using integration by parts and properties of exponential functions, the result is $e^x \cos x + C$.</p>
Correct Answer: A