AP EAMCET · Maths · Indefinite Integration
\(\int 3^{-\log _9 x^2} d x=\)
- A \(2 \log |x|+C\)
- B \(\log |x|+C\)
- C \(-\log |\mathrm{x}|+\mathrm{C}\)
- D \(-2 \log |x|+C\)
Answer & Solution
Correct Answer
(B) \(\log |x|+C\)
Step-by-step Solution
Detailed explanation
\(\int 3^{-\log _9 x^2} d x=\int 3^{\log _9\left(\frac{1}{x^2}\right)} d x\) \(=\int\left(\frac{1}{x^2}\right)^{\log _9 3} d x=\int\left(\frac{1}{x^2}\right)^{\frac{1}{2}} d x\) \(=\int \frac{1}{x} d x=\log |x|+C\).
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