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Evaluate:\(\int\cfrac{dx}{\sqrt{9x^2-7}}\)∫ dx/√(9x2-7)

Answer»

Formula to be used -\(\int\cfrac{dx}{\sqrt{x^2\pm a^2}}=log(x+\sqrt{x^2\pm a^2})+c\)

\(\therefore\int\cfrac{dx}{\sqrt{9x^2-7}}\)

\(=\int\cfrac{dx}{\sqrt{(3x)^{2}-\sqrt{7}^2}}\)

\(=log|3x+\sqrt{9x^2-7}|+c\), c being the integrating constant



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