Which Part Should I Integrate?

Calculus Level 2

Suppose that ff is a smooth function (meaning that all orders of derivatives exist and are continuous) such that f(0)=1 f(0)=1, f(2)=3f(2)=3 and f(2)=5 f' (2) = 5 , then evaluate

01xf(2x)dx. \large \int_{0}^{1} x f'' (2x)\, dx .

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