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Option D is correct , it is the direct formula.

if we place negative sign in front of option A then it will be correct to.
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At the first glance, you must be really annoyed by seeing the square roots sign. And that too in denominator !! Because square roots usually make the integrals difficult to solve.

So, let us try to eliminate this square root symbol. $x$ must be substituted by some $a.y$ such that $a^2.y^2 - a^2$ becomes a complete square and the term is able to get rid of the square root.

Trigonometric identities are the best friends. Try putting one of it in place of $y$ and you will soon find that $sec\theta$ and $cosec\theta$ are the best candidates. Just proceed with the substitution and the integral will soon simplify like anything.

Though it is not a complete answer, but I hope it helps.

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option c is correct. based on direct formula

$\int \frac{dx}{\sqrt{x^{2}}-a^{2}}= cosh^{-1}\frac{x}{a}+c$
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