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anonymous

  • 5 years ago

Can anyone think of a single integration problem that requires a combination of partial fraction decomposition, substitution, and integration by parts to be able to solve it?

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  1. cherrilyn
    • 5 years ago
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    \[\int\limits_{}^{}4-x/x(x ^{2}+2)^{2} dx\]

  2. anonymous
    • 5 years ago
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    How did you think of one so fast?

  3. cherrilyn
    • 5 years ago
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    I'm doing my calculus hw right now :)

  4. anonymous
    • 5 years ago
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    And you're saying that this problem requires knowledge from all three to solve it?

  5. cherrilyn
    • 5 years ago
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    yes

  6. dumbcow
    • 5 years ago
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    \[\int\limits_{}^{}\frac{x ^{2}}{(x+1)(x-3)} dx\]

  7. anonymous
    • 5 years ago
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    ^ how does that need integration by parts :p

  8. anonymous
    • 5 years ago
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    @ first , its not well typed for starters , but never the less , it doesnt require all 3

  9. anonymous
    • 5 years ago
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    it is prob impossible to come up with one that uses all three , well one that uses all three and can be done with elementary functions and by hand

  10. dumbcow
    • 5 years ago
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    i dunno i thought id give it a shot cant use partial fractions at first because of x^2 on top so i figured you could try splitting it up f*g f = x g = x/(x+1)(x-3)

  11. anonymous
    • 5 years ago
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    its impossible to get one that uses all three

  12. anonymous
    • 5 years ago
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    its easy to get partial fractions , but it is impossible to get partial fractions and integration by parts in the same question

  13. anonymous
    • 5 years ago
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    elecengineer, what about cherrilyn's problem?

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