Find the integral of:
x * sqrt(5x^2 - 4) * dx
Make-up
$\displaystyle \int {x\sqrt {5x^2 - 4} \,dx} = \frac{1}
{5}\int {5x\sqrt {5x^2 - 4} \,dx} .$
Set $\displaystyle u^2=5x^2-4\implies u\,du=5x\,dx,$
$\displaystyle \int {x\sqrt {5x^2 - 4} \,dx} = \frac{1}
{5}\int {u^2 \,du} = \frac{u^3 }
{{15}} + k = \frac{{\left( {5x^2 - 4} \right)^{3/2} }}
{{15}} + k.$