Intergration homework help

owl 1996

Hi
I am trying to intergrate (6x^2+27x+25)/(x+2)^2(x+1)

I split it into partial fractions
2/(2x-3)-5/(5x+2)-1/(5x+2)^2

Then integrated to give

2ln|2x-3|-5ln|5x+2|-1/(5x+2)+k

However this is not the answer in the book - can anyone tell me where I have gone wrong ? Thank you so much for any help ! :smile:

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Reply 1

ghostwalker

Original post by owl 1996

Hi
I am trying to intergrate (6x^2+27x+25)/(x+2)^2(x+1)

I split it into partial fractions
2/(2x-3)-5/(5x+2)-1/(5x+2)^2

Where did those denominators come from? They're not in your original function, so can't be in the partial fractions breakdown.

Reply 2

owl 1996

Sorry - I typed in my answer to a different question by accident . I split it uni 5/(x+2)^2 +4/(x+1)-4/(x+2)

My answer was 4ln |x+1|-4ln|x+2|-5/(x+2) +k

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Reply 3

ghostwalker

Original post by owl 1996

Sorry - I typed in my answer to a different question by accident . I split it uni 5/(x+2)^2 +4/(x+1)-4/(x+2)

My answer was 4ln |x+1|-4ln|x+2|-5/(x+2) +k

The -4/(x+2) is incorrect in the partial fractions. Other two parts are fine.

(edited 10 years ago)

Reply 4

the bear

a quick check to see if the PFs are right is to put a value into the original and split up versions... if you let x = 0

(6x^2+27x+25)/(x+2)^2(x+1) is worth 25/4

but 5/(x+2)^2 +4/(x+1)-4/(x+2) is worth 13/4.... so there is a mistake in the PFs