TS EAMCET · Maths · Indefinite Integration
\(\int \frac{3^x}{\sqrt{9^x-1}} d x=\)
- A \(\frac{1}{\log 3} \log \left|3^x+\sqrt{9^x-1}\right|+c\)
- B \(\frac{1}{\log 3} \log \left|3^x-\sqrt{9^x-1}\right|+c\)
- C \(\frac{1}{\log 9} \log \left|3^x-\sqrt{9^x-1}\right|+c\)
- D \(\frac{1}{\log 9} \log \left|9^x-\sqrt{9^x-1}\right|+c\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\log 3} \log \left|3^x+\sqrt{9^x-1}\right|+c\)
Step-by-step Solution
Detailed explanation
We have, \(\int \frac{3^x}{\sqrt{9^x-1}} d x\) Put \(3^x=t \Rightarrow 3^x \log 3 d x=d t\)…
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