Integral Calculus Question 283

Question: $ \int_{{}}^{{}}{\frac{1}{x\sqrt{x^{2}-1}}\ dx=} $

[MP PET 1988]

Options:

A) $ {{\cos }^{-1}}x+c $

B) $ {{\sec }^{-1}}x+c $

C) $ {{\cot }^{-1}}x+c $

D) $ {{\tan }^{-1}}x+c $

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Answer:

Correct Answer: B

Solution:

$ \int_{{}}^{{}}{\frac{1}{x\sqrt{x^{2}-1}},dx={{\sec }^{-1}}x+c} $ (formula).