Q112 / 160 · AP EAMCET 2023 (16 May Shift 1) · Mathematics

$\int 3^{-\log _9 x^2} d x=$

  • A
    $2 \log |x|+C$
  • Correct answer
    B
    $\log |x|+C$
  • C
    $-\log |\mathrm{x}|+\mathrm{C}$
  • D
    $-2 \log |x|+C$

Solution

$\int 3^{-\log _9 x^2} d x=\int 3^{\log _9\left(\frac{1}{x^2}\right)} d x$ $=\int\left(\frac{1}{x^2}\right)^{\log _9 3} d x=\int\left(\frac{1}{x^2}\right)^{\frac{1}{2}} d x$ $=\int \frac{1}{x} d x=\log |x|+C$.

Hence, the correct answer is option: 'B'.

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