∫ dx/x√{4x^2 - 1} =

Question

\(\int \frac{dx}{x\sqrt{4x^2 -1}}=\)

(A) sec^-1x + K

(B) sec^-12x + K

(C) 1/2 sec^-12x + K

(D) 2sec^-12x + K

Answer 1

Correct option is (C) 1/2 sec^-12x + K

\(\int \frac{dx}{x\sqrt{4x^2 -1}}= \int \frac{dx}{x\sqrt{(2x)^2 -1}}\)

\(= \frac12 \sec^{-1}2x + K\)