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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate: $\int \large\frac{1}{x \sqrt {x\log (x^2) -5}}$$dx$

$(a)\;\log | \log x^2 +\sqrt {\log x^2 -\sqrt 5}|+c\\(b)\; \log | \log x^2 +\sqrt {\log x^2 + \sqrt 5}|+c\\(c)\; 2\log | \log x^2 +\sqrt {\log x^2-\sqrt 5}|+c \\ (d)\;None$

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A)
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$\log x^2 =t$
$\large\frac{1}{x^2} $$\times 2x dx = dt$
=> $ \large\frac{1}{2x} $$dx=dt$
=> $\int \large\frac{2 dt}{\sqrt {t^2-(\sqrt 5)^2}}$
=> $ 2 \log |t+ \sqrt {t^2 - \sqrt 5} |++c$
$ 2\log | \log x^2 +\sqrt {\log x^2-\sqrt 5}|+c$
Hence c is the correct answer.
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