Power of MP test of uniform vs triangular

Let $X$ be a continuous random variable with probability density function $f(x)$. Consider the problem of testing the null hypothesis $$H_0:f(x)=\begin{cases}1& \text{if }0<x<1,\ 0& \text{otherwise,}\end{cases}$$ against the alternative hypothesis $$H_1:f(x)=\begin{cases}2x& \text{if }0<x<1,\ 0& \text{otherwise.}\end{cases}$$ Then the power of the most powerful size $\alpha$ test, where $0<\alpha<1$, based on a single sample, is