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# Integration Question! watch

1. Question: Integrate x^2 dx /((x + 1)(x^2 + x + 1))

(in words) (x squared dx) divided by (x + 1) times (x squared + x + 1)

I'm not really sure how I should start this, would I need to make a substitution or use "completing the square" on (x^2 + x + 1) then express in terms of partial fractions?
2. (Original post by As_Dust_Dances_)
Question: Integrate x^2 dx /((x + 1)(x^2 + x + 1))

(in words) (x squared dx) divided by (x + 1) times (x squared + x + 1)

I'm not really sure how I should start this, would I need to make a substitution or use "completing the square" on (x^2 + x + 1) then express in terms of partial fractions?
Observe that . Completing the square after a bit of manipulation from there is a good idea.
3. (Original post by Farhan.Hanif93)
Observe that . Completing the square after a bit of manipulation from there is a good idea.
I'm assuming then you would use partial fractions since you would get a product on the denominator?
4. (Original post by As_Dust_Dances_)
I'm assuming then you would use partial fractions since you would get a product on the denominator?
Nope. Note that ; after cancelling down, once of the terms can be integrated directly and the other can be tackled with completing the square (namely the one with x^2+x+1 in it's denominator).
5. (Original post by Farhan.Hanif93)
Nope. Note that ; after cancelling down, once of the terms can be integrated directly and the other can be tackled with completing the square (namely the one with x^2+x+1 in it's denominator).
Oh I understand now, I didn't think of expressing x^2 like that. Thanks so much for your help! + rep

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