anonymous
  • anonymous
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?
Mathematics
jamiebookeater
  • jamiebookeater
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cherrilyn
  • cherrilyn
\[\int\limits_{}^{}4-x/x(x ^{2}+2)^{2} dx\]
anonymous
  • anonymous
How did you think of one so fast?
cherrilyn
  • cherrilyn
I'm doing my calculus hw right now :)

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anonymous
  • anonymous
And you're saying that this problem requires knowledge from all three to solve it?
cherrilyn
  • cherrilyn
yes
dumbcow
  • dumbcow
\[\int\limits_{}^{}\frac{x ^{2}}{(x+1)(x-3)} dx\]
anonymous
  • anonymous
^ how does that need integration by parts :p
anonymous
  • anonymous
@ first , its not well typed for starters , but never the less , it doesnt require all 3
anonymous
  • anonymous
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
dumbcow
  • dumbcow
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)
anonymous
  • anonymous
its impossible to get one that uses all three
anonymous
  • anonymous
its easy to get partial fractions , but it is impossible to get partial fractions and integration by parts in the same question
anonymous
  • anonymous
elecengineer, what about cherrilyn's problem?

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