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Question
Using second fundamental theorem, evaluate the following:
`int_0^3 ("e"^x "d"x)/(1 + "e"^x)`
Sum
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Solution
`int_0^3 ("e"^x "d"x)/(1 + "e"^x) = {log |1 + "e"x|}_0^3`
= log |1 + e3| – log |1 + e°|
= log |1 + e3| – log |1 + 1|
= log |1 + e3| – log |2|
= `log |(1 + "e"^3)/2|`
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