Indefinite Integration
Integration of Logarithmic Functions
Grade 12
Question:
<p>86. The anti-derivative of \(f(x) = \log(\log x) + (\log x)^{-2}\) whose graph passes through \((e, e)\), is</p>
<p>(a) \(x[\log(\log x) + (\log x)^{-1}]\)</p>
<p>(b) \(x[-\log(\log x) + (\log x)^{-1}] + e\)</p>
<p>(c) \(x[\log(\log x) - (\log x)^{-1}] + 2e\)</p>
<p>(d) None of the above</p>
Step-by-Step Solution
Key Concept: Integrate using substitution or parts, then use the condition that the antiderivative passes through $(e, e)$ to find the constant of integration.
<p>Solution not provided in the source text.</p>
Correct Answer: C