To simplify the integral, let ##y=e^x## and break it into partial fractions.
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#3
Saitama
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Write e^(-x) as 1/(e^x). Simplify and you should get the expression:
[tex]\frac{e^{2x}+e^x}{e^{2x}+2e^x+1}[/tex]
Can you now see which is f(x) and which is f'(x)?