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bmelyk

  • 3 years ago

Find the indefinite integral:

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

  2. bmelyk
    • 3 years ago
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    i know i'll be using substitution.

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

  4. bmelyk
    • 3 years ago
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    e^y y dy?

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

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

  7. bmelyk
    • 3 years ago
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    well minus?

  8. TuringTest
    • 3 years ago
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    how did you get two du's ?

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

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

  11. TuringTest
    • 3 years ago
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    where is the other e^y coming from?

  12. bmelyk
    • 3 years ago
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    thats my du.

  13. bmelyk
    • 3 years ago
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    well dy.

  14. bmelyk
    • 3 years ago
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    it should be negative.

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

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

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