Using the substitution $x = \frac{1}{u}$, find \[ \displaystyle\int_{\frac{1}{2}}^{1} \frac{\mathrm{d}x}{x \sqrt{4x^2 - 1}}.\] Leave your answer in exact form.

Definite integrals by substitution

IB Year 6 | Grade 12

Using the substitution $x = \frac{1}{u}$, find
\[ \displaystyle \displaystyle\int_{\frac{1}{2}}^{1} \frac{\mathrm{d}x}{x \sqrt{4x^2 - 1}}.\]
Leave your answer in exact form.

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