Integration with an absolutely continuous function

Question

Let $u(x)$ be an absolutely continuous function on the interval $[0,1]$, and let $u(0)=0$ Prove that $$\int_0^1 \frac{|u(x)|^2}{x^{\frac{3}{2}}}dx \leq 2\int_0^1 |u'(x)|^2dx.$$ I was thinking of using integration by parts then the property that for an absolutely continuous function $f$ $$f(x)-f(a)=\int_a^x f'(t)dt$$ but I keep getting stuck and unsure if my idea is the correct method.