Evaluate:\(\int\cfrac{dx}{\sqrt{4x^2-1}}\)∫ dx/√(4x2-1)

1.	Evaluate:\(\int\cfrac{dx}{\sqrt{4x^2-1}}\)∫ dx/√(4x2-1)
Answer» Formula to be used - \(\int\cfrac{dx}{\sqrt{x^2\pm a^2}}=log(x+\sqrt{x^2\pm a^2})+c\), where c is the integrating constant \(\therefore\int\cfrac{dx}{\sqrt{4x^2-1}}\) \(= \int\cfrac{dx}{\sqrt{(2x)^{2}-1^2}}\) \(=\cfrac{1}{2}log\|2x+\sqrt{4x^2-1}\|+c\), c being the integrating constant

Answer»

Formula to be used - \(\int\cfrac{dx}{\sqrt{x^2\pm a^2}}=log(x+\sqrt{x^2\pm a^2})+c\), where c is the integrating constant

\(\therefore\int\cfrac{dx}{\sqrt{4x^2-1}}\)

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

\(=\cfrac{1}{2}log|2x+\sqrt{4x^2-1}|+c\), c being the integrating constant

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