Indefinite Integration
Exponential and Trigonometric Functions
Grade 12
Question:
<p>Evaluate \(\int e^x \sec x(1 + \tan x) dx\)</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 integrand is the derivative of $e^x \sec x$ using the product rule.
<p>Notice that $\frac{d}{dx}(e^x \sec x) = e^x \sec x + e^x \sec x \tan x = e^x \sec x(1 + \tan x)$. Therefore, the integral is $e^x \sec x + C$.</p>
Correct Answer: B