$\int {\frac{x l n x}{(x^{2} - 1)}}^{3 / 2} d x$ equals

a r c s e c x - \frac{l n x}{\sqrt{x^{2} - 1}} + C

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s e c^{- 1} x - \frac{l n x}{\sqrt{x^{2} - 1}} + C

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c o s^{- 1} x - \frac{l n x}{\sqrt{x^{2} - 1}} + C

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s e c x - \frac{l n x}{\sqrt{x^{2} - 1}} + C

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Solution

The correct option is B $s e c^{- 1} x - \frac{l n x}{\sqrt{x^{2} - 1}} + C$
I think this question is some thing
like this
$= \int \frac{x l o g x}{(x^{2} - 1)^{3 / 2}} d x$
but $x = s π θ$
$= - \int l o g (x) d (x^{2} - 1)^{- 1 / 2}$
$= \frac{- l o g x}{x^{2} - 1} + \int \frac{d x}{x \sqrt{x^{2} - 1}}$
$= \frac{- l n x}{x^{2} - 1} + s e c^{- 1} (x) + c$

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