COMEDK · Maths · 28. Indefinite Integration
\(\int \frac{9^x}{\sqrt{1-81^x}} d x\) is equal to
- A \(\sin ^{-1}\left(9^x\right)+c\)
- B \(\ln ^9 \sin ^{-1}\left(9^x\right)+c\)
- C \(\sin ^{-1}\left(81^x\right)+c\)
- D \(\frac{1}{\ln 9} \sin ^{-1}\left(9^x\right)+c\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{\ln 9} \sin ^{-1}\left(9^x\right)+c\)
Step-by-step Solution
Detailed explanation
Let \(9^x=t\) Differentiate both side w.r t. \(x\) \(\begin{aligned} 9^x \ln 9 d x & =d t \\ \Rightarrow \quad 9^x d x & =\frac{d t}{\ln 9} \end{aligned}\)…
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