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    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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    ln(2x)=lnx + ln2 = lnx + C = same as first answer
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    (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?
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    (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))

    But really yeah both of your answers are correct
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    Ah ok makes sense, thanks for clearing that up for me guys
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    (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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