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anonymous

  • 4 years ago

Integration problem: If I Integrate this \[\ \int\frac{y}{(y+1)^2}dy \] using integration by parts I get:\[\frac{-y}{y+1}+ln(y+1) \] but if I do this: \[\ \int\frac{y}{(y+1)^2}dy \] \[\ \int\frac{y+1}{(y+1)^2} -\frac{1}{(y+1)^2}dy \]and integrate I get \[\ \frac{1}{y+1} +ln(y+1)\] Sooo, what did I do wrong, what am I missing?

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  1. anonymous
    • 4 years ago
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    Dude can't you see both are one and the same thing

  2. anonymous
    • 4 years ago
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    Write -y as -y+1-1 see

  3. anonymous
    • 4 years ago
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    the second one is correct

  4. lalaly
    • 4 years ago
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    id prefer to use partial fractions or the second method u used

  5. anonymous
    • 4 years ago
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    no need for integration by parts here

  6. anonymous
    • 4 years ago
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    Just add constant of integration to both you would be surprised that after carring out what i just said you find same function with different constant of integration.... A result is consistent with what you expect out of an indefinite integration

  7. anonymous
    • 4 years ago
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    Method never changes the result it just changes the convinence of solving...

  8. anonymous
    • 4 years ago
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    Ah yes, thank you very much, this is actually a part of a bigger problem (a differential equation with given initial conditions) I didn't get the same constant C for the particular solution so i got confused, but it all works out nicely :D.

  9. anonymous
    • 4 years ago
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    "I didn't get the same constant C" like they got in the book.

  10. anonymous
    • 4 years ago
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    you said it's part of a bigger problem...my instructor spent 30 min today stressing on the importance of adding the C right away cuz waiting til the end will change it completely. for ex: dy/dx=y...add C right away and you get y=Ce^x instead of y=e^x+C

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spraguer (Moderator)
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