Let f(x)be a monotonically increasing function with continuous derivatives on the interval0,+oo],and f(0)=1,for any te0,+oo],Lines x 0,x =1,curves y=f(x)and the curvedtrapezoid formed by the X-axis rotate once around the X-axis to generate a rotating body.Ifthe side area of the rotating body is numerically equal to twice its volume,find the expressionof the function f(x).
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