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Quick C3 integration

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    Was hoping someone could help on this please, integrating with limits 1 to 9
    \large \pi \int \frac{36}{3x-2}

    I pulled out the 36 from the numerator , and made it:
    \large 36\pi \int \frac{1}{3x-2}

    \large 36\pi ln(3x-2)

    After subbing in the limits I get the answer wrong as the answer given involves 12 pi ?

    I got 36Pi ln25 , answer is 12Pi ln25 , I thought my method would usually work for these.
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    When you're integrating lnf(x), what's the rule?
  3. Offline

    The format has to be f'(x)/f(x). So you have to take out 12, as then you're left with 3 at the top (the bottom differentiates to 3). You should be fine from there on out.
  4. Offline

    notice you need a third of it
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    (Original post by RajPopat94)
    When you're integrating lnf(x), what's the rule?
    If it's 1/something, then ln(something) right ? , but I took out the 36 as a constant so that shouldn't matter ?
  6. Offline

    (Original post by Tulian)
    If it's 1/something, then ln(something) right ? , but I took out the 36 as a constant so that shouldn't matter ?
     \displaystyle \int \frac{c}{ax+b} \ dx = c \int \frac{1}{ax+b} \ dx = c \times \frac1{a} ln|ax+b| + C
  7. Offline

    I totally forgot about the 1/a part after taking the 36 out.

    Thanks everyone


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