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bmelyk

Find the indefinite integral:

  • one year ago
  • one year ago

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  1. bmelyk
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    \[\int\limits_{?}^{?}\frac{ e^{y} }{ 2-e^{y} } dy\]

    • one year ago
  2. bmelyk
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    i know i'll be using substitution.

    • one year ago
  3. TuringTest
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    Let\[u=2-e^y\]then\[du=?\]

    • one year ago
  4. bmelyk
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    e^y y dy?

    • one year ago
  5. TuringTest
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    \[u=2-e^y\implies du=-e^ydy\implies e^ydy=-du\]so what is the integral now?

    • one year ago
  6. bmelyk
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    \[\int\limits_{?}^{?} 1/du du\]

    • one year ago
  7. bmelyk
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    well minus?

    • one year ago
  8. TuringTest
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    how did you get two du's ?

    • one year ago
  9. bmelyk
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    \[\int\limits_{e^y}}^{2-e^{y}} e^{\]

    • one year ago
  10. bmelyk
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    \[\int\limits_{}^{} \frac{ e^{y} }{ 2-e{y} } e^{y}\]

    • one year ago
  11. TuringTest
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    where is the other e^y coming from?

    • one year ago
  12. bmelyk
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    thats my du.

    • one year ago
  13. bmelyk
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    well dy.

    • one year ago
  14. bmelyk
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    it should be negative.

    • one year ago
  15. bmelyk
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    is the answer ln|2-e^y|+c?

    • one year ago
  16. TuringTest
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    you dropped the negative sign, but aside from that the answer is correct

    • one year ago
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