Correct answer: B. (b) 3^- log_9 ⁡x^2 dx= 3^ log_9 ⁡ ( 1x^2 ) dx= ( 1x^2 )^ log_9 ⁡3 dx= ( 1x^2 )^ 12 dx= 1x dx= log ⁡ |x |+C .

JEE Previous Year Question

$\int 3^{- log_{9} x^{2}} dx =$

Topic: JEE PYQ

Answer: B. Full step-by-step solution below.

Correct answer: B

Solution

(b) \int 3^{- log_{9} x^{2}} dx = \int 3^{log_{9} (\frac{1}{x ^{2}})} dx = \int (\frac{1}{x ^{2}})^{log_{9} 3} dx = \int (\frac{1}{x ^{2}})^{\frac{1}{2}} dx = \int \frac{1}{x} dx = log | x | + C .