Indefinite Integration
Exponential Functions
Grade 12
Question:
<p>Evaluate: \(\int \frac{x^2 + 1}{x^2} (2\ln x + 1) dx\)</p>
<p>(a) \(x^2 + C\)</p>
<p>(b) \(x^2 \ln x + C\)</p>
<p>(c) \(x^x + C\)</p>
<p>(d) \((x^x)^x + C\)</p>
Step-by-Step Solution
Key Concept: Identify the integrand as a derivative of $x^x$ by rewriting it in proper form.
<p>This is an indefinite integration problem. Recognize that the integrand can be rewritten and solved using substitution or recognition of derivative forms.</p>
Correct Answer: C