Question

Evaluate the definite integral.
(e^x)/(7 + e^x)dx between (0,2)

Answer 1

did you not notice that the derivative of the denominator is sitting in the numerator ?
and if y = ln(u)
then dy/du = u'/u, exactly our pattern

integral of e^x/(7+e^x) from 0 to 2
= [ ln (7 + e^x) ] from 0 to 2
= ln(7 + e^2) - ln(7 + e^0)
= ln (7+e^2) - ln(7+1)
= ln ( (7+e^2)/8 )
= ...

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