Using $y=\dfrac{1}{x}$, find the exact value of \(\displaystyle\int_1^{4/3}\dfrac{5}{x\sqrt{9x^2-4

Question

Using $y=\dfrac{1}{x}$, find the exact value of $\displaystyle\int_1^{4/3}\dfrac{5}{x\sqrt{9x^2-4}}\,\mathrm{d}x$.

Accepted Answer

$\dfrac{5}{2}\left(\arcsin\dfrac{2}{3}-\dfrac{\pi}{6}\right)$

A Reciprocal Substitution