# Which Part Should I Integrate?

Calculus Level 2

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

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

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