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Question
\[\int\frac{1}{x\sqrt{4 - 9 \left( \log x \right)^2}} dx\]
Sum
Solution
\[\int\frac{dx}{x\sqrt{4 - 9 \left( \log x \right)^2}}\]
` \text{ let log x }= t `
\[ \Rightarrow \frac{1}{x} dx = dt\]
\[Now, \int\frac{dx}{x\sqrt{4 - 9 \left( \log x \right)^2}}\]
\[ = \int\frac{dt}{\sqrt{4 - 9 t^2}}\]
\[ = \int\frac{dt}{\sqrt{2^2 - \left( 3t \right)^2}}\]
\[ = \frac{1}{3} \text{ sin }^{- 1} \left( \frac{3t}{2} \right) + C\]
\[ = \frac{1}{3} \text{ sin }^{- 1} \left( \frac{3 \log x}{2} \right) + C\]
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Find: `int (sin2x)/sqrt(9 - cos^4x) dx`
