How Do I Do This ∫ 1/2e^(2x) Dx? ∫ 1/2e^(2x) …

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How Do I Do This ∫ 1/2e^(2x) Dx? ∫ 1/2e^(2x) dx
I tried to use U to do it and I got du/dx=(-4)/x
and I’m not sure if I got this part right
∫ 1/2e^(2x) dx=1/2 ∫ e^(2x) dx

I checked the book answer is f(x)=(-e^(2/x) +e^(1/2))/2+C how did they got 2 “e”?
Sorry my bad it should be ∫ 1/2e^(2/x) dx miss the “/”
So my U’ is du/dx=(-4x)/x^2=(-4)/x

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