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Question: \(\int_{}^{}{\frac{dx}{x\sqrt{1 - (\log x)^{2}}} =}\)...

∫dxx1−(log⁡x)2=\int_{}^{}{\frac{dx}{x\sqrt{1 - (\log x)^{2}}} =}

A

cos⁡−1(log⁡x)+c\cos^{- 1}(\log x) + c

B

xlog⁡(1−x2)+cx\log(1 - x^{2}) + c

C

sin⁡−1(log⁡x)+c\sin^{- 1}(\log x) + c

D

None of these

Answer

xlog⁡(1−x2)+cx\log(1 - x^{2}) + c

Explanation

Solution

1+x2+tan⁡−1x+c\sqrt{1 + x^{2}} + \tan^{- 1}x + c

1+x2−log⁡{x+1+x2}+c\sqrt{1 + x^{2}} - \log\{ x + \sqrt{1 + x^{2}}\} + c

1+x2+log⁡{x+1+x2}+c\sqrt{1 + x^{2}} + \log\{ x + \sqrt{1 + x^{2}}\} + c

1+x2+log⁡(sec⁡x+tan⁡x)+c\sqrt{1 + x^{2}} + \log(\sec x + \tan x) + c.