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?

1. cherrilyn

$\int\limits_{}^{}4-x/x(x ^{2}+2)^{2} dx$

2. anonymous

How did you think of one so fast?

3. cherrilyn

I'm doing my calculus hw right now :)

4. anonymous

And you're saying that this problem requires knowledge from all three to solve it?

5. cherrilyn

yes

6. dumbcow

$\int\limits_{}^{}\frac{x ^{2}}{(x+1)(x-3)} dx$

7. anonymous

^ how does that need integration by parts :p

8. anonymous

@ first , its not well typed for starters , but never the less , it doesnt require all 3

9. 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

10. 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)

11. anonymous

its impossible to get one that uses all three

12. anonymous

its easy to get partial fractions , but it is impossible to get partial fractions and integration by parts in the same question

13. anonymous