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Jarhead1

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I'm new to this forum. This semester I took Calculus I and just took the final yesterday. There were a few questions that were unexpected that I didn't know how to handle. This integral has got me stumped.\(\displaystyle \int_{0}^{1} e^{x}/(1 + e^{2x}) \,dx\)

The techniques I know at this point include u substitution and the table of integral rules which I'm sure is limited at this point. \(\displaystyle \int e^{x}dx\) is \(\displaystyle e^{x}+C\) but that doesn't help with \(\displaystyle 1/ (1 + e^{2x})\). I tried u sub of \(\displaystyle u = 1 + e^{2x}\) but \(\displaystyle du/2e^{2x} = dx \) doesn't help. I end up with this integral with a u sub and \(\displaystyle e^{-x}\) .

\(\displaystyle 1/2 \int_{0}^{1} 1/u \cdot e^{-x} \,du\) Note: \(\displaystyle e^{x}/e^{2x} = e^{-x}\)

Maybe there is a technique we haven't learned yet or I missed something.

Thanks in advance