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# FP2 Edexcel problem - Integration watch

1. this question is gonna look messy so if anyone has the heinemann fp2 edexcel book then it is exercise 3B, question 17.

it asks me to integrate 1/(2(x^2)+7x+3)dx

by completing the square, i end up with:

0.2ln[(x+0.5)/(x+3)] + C

the answer at the back of the book is:

0.2ln[(2x+1)/(x+3)] + C

if i integrate using partial fractions i get the same answer at the back of the book. I'm really confused because i thought both methods are good to use. it goes without saying i will use the partial fractions method where possible, despite being longer. however i would love it if someone would explain why this happens (it seems to happen with all integrals of this type, where the coefficient of x^2 isn't one). another example can be found in exercise 3C, question 16 of the same book.
any help would be greatly appreciated.
2. 0.2ln[(2x+1)/(x+3)] + C = 0.2ln(2*(x+0.5)/(x+3)) + C
= 0.2ln2 + 0.2ln[(x+0.5)/(x+3)] + C = your answer with different integration constant.
3. (Original post by Speleo)
0.2ln[(2x+1)/(x+3)] + C = 0.2ln(2*(x+0.5)/(x+3)) + C
= 0.2ln2 + 0.2ln[(x+0.5)/(x+3)] + C = your answer with different integration constant.

so really the constant is: 0.2ln2 + C ?
surely both functions would have different answers if limits were applied?
4. C represents two different numbers in each expression.
In the two different expressions, C = D (say) for one, and C = D - 0.2ln2 for the other.

Also, substituting the limits of the integral into F(x) and F(x) + A where A is a constant gives the same answer.

e.g. [x^2]0->1 = (1) - (0) = 1
[x^2 + 10,000,000]0->1 = (10,000,001) - (10,000,000) = 1

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Updated: October 23, 2006
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