Efficiently Solve ∫x^2/(x^2+4x+8)dx with Expert Tips | Integral Practice

[bpatrick]

Homework Statement

∫x^2/(x^2+4x+8)dx

Homework Equations

N/A

The Attempt at a Solution

I've tried a few things so far and nothing clicked, I may be just missing something obvious ... if anybody sees the solution and could just give me the first step or a hint, that would be sweet ... this isn't for homework or a class or anything, just a HUGE list of integrals that was given to me a month or so ago via a kind sir on this forum so I could do a few integrals each day for practice. This one (pretty sure) was on the 2nd page of the list and I'm now on the 4th page, but it has been on a little post-it for the last two weeks since I haven't been able to figure it out as I kept going through the rest of the list.

Any help is appreciated.

 

[Mark44]

Homework Statement

∫x^2/(x^2+4x+8)dx

Homework Equations

N/A

The Attempt at a Solution

I've tried a few things so far and nothing clicked, I may be just missing something obvious ... if anybody sees the solution and could just give me the first step or a hint, that would be sweet ... this isn't for homework or a class or anything, just a HUGE list of integrals that was given to me a month or so ago via a kind sir on this forum so I could do a few integrals each day for practice. This one (pretty sure) was on the 2nd page of the list and I'm now on the 4th page, but it has been on a little post-it for the last two weeks since I haven't been able to figure it out as I kept going through the rest of the list.

Any help is appreciated.

x²/(x² + 4x + 8) is an improper rational function. I would start by using polynomial long division to rewrite the integrand as 1 + <proper rational function>.

 

[bpatrick]

thanks, got it within 2 minutes of reading that ... knew I was just missing something simple.

x + ln(x^2+4x+8) + c