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# Help with integration Please explain. watch

1. To find the integral of 3/(9-x^(2)) why is it wrong to have (-3/2x)ln(9-x^2)) as the answer?? markscheme says (-1/2)ln(3-x)+(1/2)ln(3+x)
2. Basically start with the equation 3/(9-x^(2)) and do partial fractions so it comes out as 3 = A(3+x) +B(3-x)
Then do when x=2: 3 = 5A+B so B = 3 - 5A
Then when x = 0: 3 = 3A +3B
Substitute B = 3-5A to get A = 1/2 and B = 1/2
So now the question is integrate 1/2(3-x)+1/2(3-x)
take the 1/2 out and integrate 1/(3-x) which give -ln(3-x). With the 1/2 it's -1/2ln(3-x)
same with the other so it's 1/2ln(3+x)
So the answer is -1/2ln(3-x)+1/2ln(3+x) + C
3. (Original post by MWills99)
Basically start with the equation 3/(9-x^(2)) and do partial fractions so it comes out as 3 = A(3+x) +B(3-x)
Then do when x=2: 3 = 5A+B so B = 3 - 5A
Then when x = 0: 3 = 3A +3B
Substitute B = 3-5A to get A = 1/2 and B = 1/2
So now the question is integrate 1/2(3-x)+1/2(3-x)
take the 1/2 out and integrate 1/(3-x) which give -ln(3-x). With the 1/2 it's -1/2ln(3-x)
same with the other so it's 1/2ln(3+x)
So the answer is -1/2ln(3-x)+1/2ln(3+x) + C
i understand this but i just want to understand why my method won't work
4. (Original post by MrToodles4)
To find the integral of 3/(9-x^(2)) why is it wrong to have (-3/2x)ln(9-x^2)) as the answer?? markscheme says (-1/2)ln(3-x)+(1/2)ln(3+x)
Integration is the reverse of differentiation (another name for an integral is an antiderivative). So by differentiating your integral, you should get back the original function. Try differentiating what you got and see if that works.
5. (Original post by MrToodles4)
i understand this but i just want to understand why my method won't work
6. (Original post by MrToodles4)
i understand this but i just want to understand why my method won't work
You're trying to use a rule that only works for linear functions to a denominator that isn't linear. It's really important to understand all the methods you're using and not just apply them to random integrals.

If you try differentiating your answer then you'll see it doesn't work.

Also try using substitution for e.g. 3/(x+2) with u = x+2 then try using it for your integral with u = 9-x^2 and you'll see the difference.

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Updated: February 24, 2018
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