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Help with AL Maths question

Show that the integral of 6+6x all over (2-x)(2+x^2) is 3ln3 and the limits are 1 and -1. I'm struggling with the bracket (2+x squared) and how i would set that to zero and use that. Some help would be appreciated!
Reply 1
Partial fractions is the way to go, so upload what youve tried/ / what youre stuck with.

If youre trying to solve for the coefficients (make the bracket zero ...) then you can compare coefficients as well to determine the value.
(edited 9 months ago)
Reply 2
Original post by pigeonwarrior
Show that the integral of 6+6x all over (2-x)(2+x^2) is 3ln3 and the limits are 1 and -1. I'm struggling with the bracket (2+x squared) and how i would set that to zero and use that. Some help would be appreciated!

as well as mqb's suggestion you can plug in any value for x e.g. x= 0, x= -1 that makes the expressions easy to evaluate and then solve some simple linear equations in the coefficients. All these methods should lead to the same result :smile:
Thank youu to the both of you I think I get it now! :smile:
It's just that I hadn't seen a question like that before
Reply 4
Original post by pigeonwarrior
Thank youu to the both of you I think I get it now! :smile:
It's just that I hadn't seen a question like that before

When you say "a question like that", what do you mean exactly? Presumably you've done other partial fractions questions where the denominator has 2 simple linear factors like (x + A)(x + B), so is it just the presence of a quadratic factor that doesn't factorise that's confusing you? Any decent textbook or website that covers partial fractions should have a few examples of this :smile:
Original post by davros
When you say "a question like that", what do you mean exactly? Presumably you've done other partial fractions questions where the denominator has 2 simple linear factors like (x + A)(x + B), so is it just the presence of a quadratic factor that doesn't factorise that's confusing you? Any decent textbook or website that covers partial fractions should have a few examples of this :smile:

Ahh yess you're right! I'm repeating maths with a different board so this type of question was new to me :smile:
it was the (2+x squared) that confused me a bit but I undertsand what to do with it now!
Thank you!!

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