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?

Question

cherrilyn · Answer

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

anonymous · Answer

How did you think of one so fast?

cherrilyn · Answer

I'm doing my calculus hw right now :)

anonymous · Answer

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

cherrilyn · Answer

yes

dumbcow · Answer

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

anonymous · Answer

^ how does that need integration by parts :p

anonymous · Answer

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

anonymous · Answer

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 · Answer

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 · Answer

its impossible to get one that uses all three

anonymous · Answer

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

anonymous · Answer

elecengineer, what about cherrilyn's problem?