Indefinite Integration
Special Forms
Grade 12
Question:
<p>Evaluate \(\int e^x dx\)</p>
<p>(a) \(e^x\left(\frac{x}{x+4}\right) + C\)</p>
<p>(b) \(e^x\left(\frac{x+2}{x+4}\right) + C\)</p>
<p>(c) \(e^x\left(\frac{x-2}{x+4}\right) + C\)</p>
<p>(d) \(2xe^x + C\)</p>
Step-by-Step Solution
Key Concept: When integrating exponential times a rational function, look for patterns or use repeated integration by parts.
<p>For integrals of the form $\int e^x \cdot P(x) dx$ where $P(x)$ is rational, use integration by parts or recognize patterns. The result is $e^x\left(\frac{x+2}{x+4}\right) + C$.</p>
Correct Answer: B