How do you integrate e^(-st)f(t) in the Laplace transform definition?

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lostinhere
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This question may be obvious but I am stumped. I know the definition of a Laplace Transform is integration of e^(-st)f(t). However, I don't know how to integrate with both s and t variables included. If anyone could provide insight I would appreciated it.
 
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The integration is only over the variable t and you treat s as a constant.
 
thanks, I knew it was simple