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# integration question

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1. So I have solved the problem using method 1 which is correct, and for method 2 I have rewritten the problem so the numerator is the denominator differentiated and followed this rule when integrating. Why then is the subsequent answer incorrect?

I know it's a bit silly but can someone please clarify what's going on here, thanks
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2. ln(2x)=lnx + ln2 = lnx + C = same as first answer
3. (Original post by L-Tyrosine)
ln(2x)=lnx + ln2 = lnx + C = same as first answer
So the constant of integration is just different on each answer?

So if I did this in an exam it would be acceptable?
4. (Original post by Katiee224)
So I have solved the problem using method 1 which is correct, and for method 2 I have rewritten the problem so the numerator is the denominator differentiated and followed this rule when integrating. Why then is the subsequent answer incorrect?

I know it's a bit silly but can someone please clarify what's going on here, thanks
½ln(2x) is correct
If we let u=2x
Then du/dx = 2
Which implies dx = ½du
So we can the integral of ½ u^-1 du
Which is ½lnu
As u=2x
We get ½ln2x

Or if you'd rather the integral of f'(x)/f(x) dx = ln(f(x))

5. Ah ok makes sense, thanks for clearing that up for me guys
6. (Original post by Katiee224)
Ah ok makes sense, thanks for clearing that up for me guys
also don't forget to put the modulus signs round the underneath...

ln|2x| + c

etc

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