anonymous
  • anonymous
Find the indefinite integral:
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
\[\int\limits_{?}^{?}\frac{ e^{y} }{ 2-e^{y} } dy\]
anonymous
  • anonymous
i know i'll be using substitution.
TuringTest
  • TuringTest
Let\[u=2-e^y\]then\[du=?\]

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anonymous
  • anonymous
e^y y dy?
TuringTest
  • TuringTest
\[u=2-e^y\implies du=-e^ydy\implies e^ydy=-du\]so what is the integral now?
anonymous
  • anonymous
\[\int\limits_{?}^{?} 1/du du\]
anonymous
  • anonymous
well minus?
TuringTest
  • TuringTest
how did you get two du's ?
anonymous
  • anonymous
\[\int\limits_{e^y}}^{2-e^{y}} e^{\]
anonymous
  • anonymous
\[\int\limits_{}^{} \frac{ e^{y} }{ 2-e{y} } e^{y}\]
TuringTest
  • TuringTest
where is the other e^y coming from?
anonymous
  • anonymous
thats my du.
anonymous
  • anonymous
well dy.
anonymous
  • anonymous
it should be negative.
anonymous
  • anonymous
is the answer ln|2-e^y|+c?
TuringTest
  • TuringTest
you dropped the negative sign, but aside from that the answer is correct

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